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Simple Interest (SI)

Topic: Simple and Compound InterestChapter: Chapter 4
SI=P×R×T100SI = \frac{P \times R \times T}{100}
This formula calculates the interest earned or paid only on the principal amount. P represents the Principal amount, R is the Rate of Interest per annum (in percentage), and T is the Time period (in years). It is used when interest is not reinvested or compounded.

Amount (A) for Simple Interest

Topic: Simple and Compound InterestChapter: Chapter 4
A=P+SIorA=P(1+R×T100)A = P + SI \quad \text{or} \quad A = P \left(1 + \frac{R \times T}{100}\right)
This formula calculates the total amount (Principal + Simple Interest) receivable or payable at the end of the period. P is the Principal, SI is the Simple Interest, R is the Rate of Interest per annum, and T is the Time period in years.

Compound Interest (CI)

Topic: Simple and Compound InterestChapter: Chapter 4
CI=A−PorCI=P[(1+R100)T−1]CI = A - P \quad \text{or} \quad CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right]
Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. P is the Principal, R is the Rate of Interest per annum, and T is the Time period in years. This formula assumes annual compounding.

Amount (A) for Compound Interest (Annual Compounding)

Topic: Simple and Compound InterestChapter: Chapter 4
A=P(1+R100)TA = P \left(1 + \frac{R}{100}\right)^T
This formula calculates the total amount (Principal + Compound Interest) when interest is compounded annually. P is the Principal, R is the Rate of Interest per annum (in percentage), and T is the Time period in years.

Amount (A) for Compound Interest (Compounded 'm' times a year)

Topic: Simple and Compound InterestChapter: Chapter 4
A=P(1+Rm×100)m×TA = P \left(1 + \frac{R}{m \times 100}\right)^{m \times T}
This formula is used when interest is compounded more frequently than once a year (e.g., semi-annually, quarterly, monthly). P is the Principal, R is the annual Rate of Interest, T is the Time period in years, and 'm' is the number of compounding periods per year (e.g., m=2 for semi-annual, m=4 for quarterly, m=12 for monthly).

Effective Rate of Interest (ERI)

Topic: Simple and Compound InterestChapter: Chapter 4
ERI=[(1+Rm×100)m−1]×100ERI = \left[\left(1 + \frac{R}{m \times 100}\right)^m - 1\right] \times 100
The Effective Rate of Interest (ERI) is the actual annual rate of interest earned or paid, considering the effect of compounding. R is the nominal annual rate of interest, and 'm' is the number of compounding periods per year. It helps compare different interest rates with varying compounding frequencies.

Present Value (PV) for Compound Interest (Discounting)

Topic: Simple and Compound InterestChapter: Chapter 4
PV=A(1+R100)TorPV=A(1+R100)−TPV = \frac{A}{\left(1 + \frac{R}{100}\right)^T} \quad \text{or} \quad PV = A \left(1 + \frac{R}{100}\right)^{-T}
This formula calculates the present value of a future amount (A) when discounted at a compound interest rate. It helps determine how much needs to be invested today to achieve a certain future value. A is the Future Value, R is the discount Rate per annum, and T is the Time period in years.

Future Value of an Ordinary Annuity (FVOA)

Topic: AnnuitiesChapter: Chapter 4
FV=P[(1+i)n−1i]FV = P \left[ \frac{(1+i)^n - 1}{i} \right]
This formula calculates the total accumulated value of a series of equal payments (P) made at the end of each period, compounded at an interest rate (i) per period, over 'n' periods. It is used when payments are made at the end of each interval.

Present Value of an Ordinary Annuity (PVOA)

Topic: AnnuitiesChapter: Chapter 4
PV=P[1−(1+i)−ni]PV = P \left[ \frac{1 - (1+i)^{-n}}{i} \right]
This formula determines the current worth of a series of equal payments (P) to be received at the end of each period, discounted at an interest rate (i) per period, over 'n' periods. It is used to find the lump sum equivalent of future periodic payments.

Future Value of an Annuity Due (FVAD)

Topic: AnnuitiesChapter: Chapter 4
FVdue=P[(1+i)n−1i](1+i)FV_{due} = P \left[ \frac{(1+i)^n - 1}{i} \right] (1+i)
This formula calculates the total accumulated value of a series of equal payments (P) made at the beginning of each period, compounded at an interest rate (i) per period, over 'n' periods. It is essentially the FVOA multiplied by (1+i) because each payment earns interest for one extra period.

Present Value of an Annuity Due (PVAD)

Topic: AnnuitiesChapter: Chapter 4
PVdue=P[1−(1+i)−ni](1+i)PV_{due} = P \left[ \frac{1 - (1+i)^{-n}}{i} \right] (1+i)
This formula determines the current worth of a series of equal payments (P) to be received at the beginning of each period, discounted at an interest rate (i) per period, over 'n' periods. It is the PVOA multiplied by (1+i) as each payment is received one period earlier, thus discounted for one less period.

Present Value of a Perpetuity

Topic: AnnuitiesChapter: Chapter 4
PV=PiPV = \frac{P}{i}
This formula calculates the present value of an infinite series of equal payments (P) that are received at the end of each period, discounted at an interest rate (i) per period. It is used for investments that promise perpetual returns.

Sinking Fund Factor (SFF)

Topic: AnnuitiesChapter: Chapter 4
P=FV[i(1+i)n−1]P = FV \left[ \frac{i}{(1+i)^n - 1} \right]
This formula calculates the periodic payment (P) required to accumulate a specific future sum (FV) at a given interest rate (i) over 'n' periods. It is the reciprocal of the Future Value of an Ordinary Annuity factor and is used for creating a sinking fund.

Capital Recovery Factor (CRF)

Topic: AnnuitiesChapter: Chapter 4
P=PV[i1−(1+i)−n]P = PV \left[ \frac{i}{1 - (1+i)^{-n}} \right]
This formula calculates the equal periodic payment (P) required to amortize a loan or recover an initial capital investment (PV) over 'n' periods at an interest rate (i). It is the reciprocal of the Present Value of an Ordinary Annuity factor.

Simple Interest (SI)

Topic: Logical ReasoningChapter: Chapter 4
SI=P×R×T100SI = \frac{P \times R \times T}{100}
P = Principal amount, R = Rate of Interest per annum (in percentage), T = Time period in years. This formula calculates interest only on the initial principal amount.

Amount (Simple Interest)

Topic: Logical ReasoningChapter: Chapter 4
A=P+SI=P(1+R×T100)A = P + SI = P \left(1 + \frac{R \times T}{100}\right)
A = Total Amount, P = Principal, SI = Simple Interest. This is the total sum accumulated after adding simple interest to the principal.

Compound Interest (CI)

Topic: Logical ReasoningChapter: Chapter 4
CI=P(1+R100)T−PCI = P \left(1 + \frac{R}{100}\right)^T - P
P = Principal amount, R = Rate of Interest per compounding period (in percentage), T = Total number of compounding periods. Interest is calculated on the principal and also on the accumulated interest from previous periods.

Amount (Compound Interest)

Topic: Logical ReasoningChapter: Chapter 4
A=P(1+R100)TA = P \left(1 + \frac{R}{100}\right)^T
A = Total Amount, P = Principal, R = Rate of Interest per compounding period (in percentage), T = Total number of compounding periods. This is the total sum accumulated after adding compound interest to the principal.

Effective Annual Rate (EAR)

Topic: Logical ReasoningChapter: Chapter 4
EAR=(1+in)n−1EAR = \left(1 + \frac{i}{n}\right)^n - 1
i = Nominal annual interest rate (as a decimal), n = Number of compounding periods per year. This formula calculates the actual annual rate of return, taking into account the effect of compounding more frequently than once a year.

Present Value of an Annuity Regular (PVA)

Topic: Logical ReasoningChapter: Chapter 4
PVA=PMT[1−(1+i)−ni]PVA = PMT \left[ \frac{1 - (1 + i)^{-n}}{i} \right]
PMT = Payment per period, i = Interest rate per period (as a decimal), n = Total number of periods. Used to find the current value of a series of equal payments made at the end of each period.

Future Value of an Annuity Regular (FVA)

Topic: Logical ReasoningChapter: Chapter 4
FVA=PMT[(1+i)n−1i]FVA = PMT \left[ \frac{(1 + i)^n - 1}{i} \right]
PMT = Payment per period, i = Interest rate per period (as a decimal), n = Total number of periods. Used to find the future value of a series of equal payments made at the end of each period.

Present Value of an Annuity Due (PVAD)

Topic: Logical ReasoningChapter: Chapter 4
PVAD=PMT[1−(1+i)−ni](1+i)PVAD = PMT \left[ \frac{1 - (1 + i)^{-n}}{i} \right] (1 + i)
PMT = Payment per period, i = Interest rate per period (as a decimal), n = Total number of periods. Used to find the current value of a series of equal payments made at the beginning of each period.

Future Value of an Annuity Due (FVAD)

Topic: Logical ReasoningChapter: Chapter 4
FVAD=PMT[(1+i)n−1i](1+i)FVAD = PMT \left[ \frac{(1 + i)^n - 1}{i} \right] (1 + i)
PMT = Payment per period, i = Interest rate per period (as a decimal), n = Total number of periods. Used to find the future value of a series of equal payments made at the beginning of each period.

Present Value of a Perpetuity

Topic: Logical ReasoningChapter: Chapter 4
PV=PMTiPV = \frac{PMT}{i}
PMT = Payment per period, i = Interest rate per period (as a decimal). Used to find the current value of an infinite series of equal payments.

Simple Interest (SI)

Topic: Time Value of MoneyChapter: Chapter 4
SI=P×R×T100SI = \frac{P \times R \times T}{100}
This formula calculates the interest earned or paid on the principal amount only. 'P' is the Principal amount, 'R' is the Rate of interest per annum, and 'T' is the Time period in years. It's used for short-term calculations where interest is not compounded.

Amount (A) for Simple Interest

Topic: Time Value of MoneyChapter: Chapter 4
A=P+SIorA=P(1+R×T100)A = P + SI \quad \text{or} \quad A = P \left(1 + \frac{R \times T}{100}\right)
This formula calculates the total amount (Principal + Interest) after a given period under simple interest. 'A' is the Amount, 'P' is the Principal, 'SI' is Simple Interest, 'R' is the Rate of interest per annum, and 'T' is the Time period in years.

Compound Interest (CI) - Future Value (FV)

Topic: Time Value of MoneyChapter: Chapter 4
FV=P(1+in)n×tFV = P \left(1 + \frac{i}{n}\right)^{n \times t}
This formula calculates the future value of a principal amount 'P' invested for 't' years at an annual interest rate 'i' (as a decimal), compounded 'n' times per year. It accounts for interest earned on both the initial principal and accumulated interest from previous periods.

Compound Interest (CI) - Present Value (PV)

Topic: Time Value of MoneyChapter: Chapter 4
PV=FV(1+in)n×torPV=FV(1+in)−n×tPV = \frac{FV}{\left(1 + \frac{i}{n}\right)^{n \times t}} \quad \text{or} \quad PV = FV \left(1 + \frac{i}{n}\right)^{-n \times t}
This formula calculates the present value of a future amount 'FV' that will be received 't' years from now, discounted at an annual interest rate 'i' (as a decimal), compounded 'n' times per year. It's used to determine how much needs to be invested today to achieve a future sum.

Effective Annual Rate (EAR)

Topic: Time Value of MoneyChapter: Chapter 4
EAR=(1+in)n−1EAR = \left(1 + \frac{i}{n}\right)^n - 1
This formula calculates the actual annual rate of interest earned or paid, considering the effect of compounding more frequently than once a year. 'i' is the nominal annual interest rate (as a decimal), and 'n' is the number of compounding periods per year. It allows for comparison of different interest rates with varying compounding frequencies.

Future Value of an Ordinary Annuity (FVA_ord)

Topic: Time Value of MoneyChapter: Chapter 4
FVAord=PMT[(1+i)t−1i]FVA_{\text{ord}} = PMT \left[ \frac{\left(1 + i\right)^t - 1}{i} \right]
This formula calculates the future value of a series of equal payments (PMT) made at the end of each period for 't' periods, earning an interest rate 'i' per period. An ordinary annuity assumes payments occur at the end of each period.

Present Value of an Ordinary Annuity (PVA_ord)

Topic: Time Value of MoneyChapter: Chapter 4
PVAord=PMT[1−(1+i)−ti]PVA_{\text{ord}} = PMT \left[ \frac{1 - \left(1 + i\right)^{-t}}{i} \right]
This formula calculates the present value of a series of equal payments (PMT) received at the end of each period for 't' periods, discounted at an interest rate 'i' per period. It's used to determine the lump sum amount today that is equivalent to a future stream of payments.

Future Value of an Annuity Due (FVA_due)

Topic: Time Value of MoneyChapter: Chapter 4
FVAdue=PMT[(1+i)t−1i](1+i)FVA_{\text{due}} = PMT \left[ \frac{\left(1 + i\right)^t - 1}{i} \right] \left(1 + i\right)
This formula calculates the future value of a series of equal payments (PMT) made at the beginning of each period for 't' periods, earning an interest rate 'i' per period. An annuity due assumes payments occur at the beginning of each period, hence the additional compounding factor of (1+i).

Present Value of an Annuity Due (PVA_due)

Topic: Time Value of MoneyChapter: Chapter 4
PVAdue=PMT[1−(1+i)−ti](1+i)PVA_{\text{due}} = PMT \left[ \frac{1 - \left(1 + i\right)^{-t}}{i} \right] \left(1 + i\right)
This formula calculates the present value of a series of equal payments (PMT) received at the beginning of each period for 't' periods, discounted at an interest rate 'i' per period. Similar to ordinary annuity PV, but adjusted for payments at the start of the period.

Present Value of a Perpetuity (PV_perp)

Topic: Time Value of MoneyChapter: Chapter 4
PVperp=PMTiPV_{\text{perp}} = \frac{PMT}{i}
This formula calculates the present value of an infinite series of equal payments (PMT) received at the end of each period, discounted at an interest rate 'i' per period. It's used for investments that promise to pay a fixed amount forever, such as certain types of bonds or preferred stocks.
Chapter 4 Formulas — CA Foundation | Kartavvya