ISD 151 BUSINESS MATHEMATICS COMPOUND INTEREST AND PRESENT

ISD 151: BUSINESS MATHEMATICS COMPOUND INTEREST AND PRESENT VALUE

OUTLINE Definition of Compound Interest Determining Compound Periods Computing Present Values Daily and Continuous Compounding

Compound Interest Compound interest is a kind of interest that is calculated on both principal and interest accrued once or more than once in a specified period. Unlike simple interest that is calculated once a year (p. a. ) and only the principal, compound interest is calculated on both the principal and the interest any number of times agreed upon in a given period. This means that under compound interest, the interest from the previous period is treated as part of principal and interest is calculated on the total sum in the next

If an investment is compounded annually for 2 years, First, the simple interest on the principal is calculated at the end of the first year. Second, the interest earned at the end of the first year is added to the principal to serve as the principal at the beginning of the second year. At the end of the 2 nd year, interest is calculated on this new principal and not the old. The total value of an investment is hence the principal plus all the compound interest and this is called the future value or compound amount

Example invests Ȼ 2000 for 2 years in an account that pays 6% interest compounded annually. Compute the total compound interest and future value of the investment. Solution 1 st year interest = Ȼ 2000 x 0. 06 x 1 = Ȼ 120 2 nd year principal = Ȼ 2000 + Ȼ 120 = Ȼ 2120 So 2 nd year interest = Ȼ 2120 x 0. 06 x 1 = Ȼ 127. 20 Total compound interest = Ȼ 120 + Ȼ 127. 20 = Ȼ 247. 20 Future value = Ȼ 2000 + 120 + Ȼ 127. 20 =Ȼ 2, 247. 20 Robert

Computing Future Value (FV) The future value of an investment can be determined using the formula: FV = Principal (PV) x Future value factor (FVF) The FVF can be read from the interest table or computed using the formula: (1 + r)n r = interest rate/ cost of capital n = number of compounding periods

Determining the Number of Compounding Periods and Periodic Rates Compound interest can be charged daily (everyday), monthly (every month), quarterly (every quarter), semiannually (every halfyear), or annually (once a year) The “period” is the unit of time of the compounding, and the periodic rate is the rate of interest corresponding to the periods. To obtain the periodic rate, we: 1. Determine the number of corresponding periods in 1 year. (i. e. m = 1 for annually; m=2 for semiannually – 12 months/6 months)

2. Divide the stated annual rate (r) by the number of periods in 1 year (m). The quotient is the periodic is rate (i). m/r = I 3. Multiply the number of periods in 1 year (m) by the number of years (t). The product is the total number of compounding periods n. NB: The annual rate is called the “nominal rate” and the “effective rate” is the true annual yield an investment makes if the interest is compounded more than once.

Computing Present Value Usually businesses have to make investments whose outcome is not immediately known. To be able to determine whether these investments are worth it or not, they have to calculate the present value to those investments. Pv = fv/(1 + r)n Pv = fv/(1 + r + p)n P = Inflation rate (i. e. if inflation is not added to the computation of r.

Example Musah and Co. made an investment that is expected to yield GHc 12, 000. 00 in three years per annum. Determine the present value of this investment if the interest rate is 18%. Solution: Pv = fv/ (1 + r)n fv = 12, 000 r = 18% or 0. 18 n = 3 Pv = 12000/ (1 + 0. 18)3 = 12000/1. 6430 1. Pv = 7303. 71