If you invest 1000 for 20 years at an 8 nominal annual inter

If you invest $1000 for 20 years at an 8% nominal annual interest rate how much will you earn with monthly compounding? Daily compounding? Weekly compounding? How much difference is there between daily and weekly compounding? How much is the difference between the monthly and the daily compounding earnings?

Solution

For compounding, we divide interest rate by compounding factor and multiply time by compounding factor.

FV = P(1+i)^n

P = $1000, n = 20, I = 8%

For monthly compounding,

FV = 1000(1+8%/12)^20*12

FV = 4926.80

Earning = 4926.80-1000 = 3926.80

For Daily compounding,

FV = 1000*(1+8%/365)^20*365

Fv = 4952.16

Earning = 4952.16-1000 = 3952.16

For weekly compounding

FV = 1000*(1+8%/52)^20*52

FV = 4946.95

Earnings = 4946.95-1000 = 3946.95

Difference Daily & weekly

= 3952.16-3946.95 = 5.21

Difference Monthly & Daily

= 3926.80-3952.16 = 25.36