Question

You just received a bonus of $3,000. a. Calculate the future value of $ 3,000, given that it will be held in the bank for 8 years and earn an annual interest rate of 3 percent. b. Recalculate part (a ) using a compounding period that is (1) semiannual and (2) bimonthly. c. Recalculate parts (a ) and (b ) using an annual interest rate of 6 percent. d. Recalculate part (a ) using a time horizon of 16 years at an annual interest rate of 3 percent. e. What conclusions can you draw when you compare the answers in parts (c ) and (d ) with the answers in parts (a ) and (b )?

Answer 1

a.

Formula for compound interest:

A = P x (1 + r/m) ^mt

A = Future value of investment

P = Principal = $ 3,000

r = Rate of interest = 3 %

m = No. of compounding in a year = 1

t = No. of years = 8

A = $ 3,000 x (1+0.03)⁸

    = $ 3,000 x (1.03)⁸

    = $ 3,000 x 1.26677008138762

    = $ 3,800.31024416285 or $ 3,800.31

b.

1.

m = No. of compounding in a year = 2

A = $ 3,000 x (1+0.03/2)^8x2

    = $ 3,000 x (1.015)¹⁶

    = $ 3,000 x 1.26898554765418

    = $ 3,806.95664296255 or $ 3,806.96

2.

m = No. of compounding in a year = 24

A = $ 3,000 x (1+0.03/24)^8x24

   = $ 3,000 x (1+0.00125)¹⁹²

   = $ 3,000 x (1.00125)¹⁹²

   = $ 3,000 x 1.2710586359832

    = $ 3,813.17590794961 or $ 3,813.18

c.

Formula for compound interest:

A = P x (1 + r/m) ^mt

A = Future value of investment

P = Principal = $ 3,000

r = Rate of interest = 6 %

m = No. of compounding in a year = 1

t = No. of years = 8

A = $ 3,000 x (1+0.06)⁸

    = $ 3,000 x (1.06)⁸

    = $ 3,000 x 1.59384807453084

    = $ 4,781.54422359253 or $ 4,781.54

1.

m = No. of compounding in a year = 2

A = $ 3,000 x (1+0.06/2)^8x2

    = $ 3,000 x (1.03)¹⁶

    = $ 3,000 x 1.60470643909879

    = $ 4,814.11931729636 or $ 4,814.12

2.

m = No. of compounding in a year = 24

A = $ 3,000 x (1+0.06/24)^8x24

   = $ 3,000 x (1+0.0025)¹⁹²

   = $ 3,000 x (1.0025)¹⁹²

   = $ 3,000 x 1.6151066604704

   = $ 4,845.31998141108 or $ 4,845.32

d.

t = 16 years

A = P x (1 + r/m) ^mt

A = $ 3,000 x (1+0.03)¹⁶

    = $ 3,000 x (1.03)¹⁶

    = $ 3,000 x 1.60470643909879

    = $ 4,814.11931729636 or $ 4,814.12

e.

From all the above answers it is concluded that future value of investment increases on increasing interest rate and also increases with number of periods and compounding frequency. In other word future value of investment varies directly with interest rate, number of periods and compounding frequency in a year.