Question

. Mark saves $20 at the end of each week and deposits the money in an account paying 4% compounded monthly. a. How much will he accumulate in 10 years? _______________ b. How much of the accumulated amount is interest? _______________

Answer 1

Amount saved at the end of each week = $20

Interest Rate = 4% compounde Monthly.

Calculating the Interest Rate compounded weekly using EAR formula of compounded monthlly:-

where, r1 = Interest rate compounded weekly

m1 = No of times compounding in a year = 52

r2 = Interest rate compounded monthly = 4%

m2 = No of times compounding in a year = 12

Taking 52-root on both sides,

r1 = 3.99464%

a). Calculalting the Future Value of Weekly savings:-

Where, C= Periodic Savings = $20

r = Periodic Interest rate = 3.99464%52 = 0.07682%

n= no of periods = 10 years*52 = 520

Future Value = $12,777.84

So, Accumulated Value in 10 years is $12,777.84

b). Accumulated Amount in Interest = Future Value - (No of Payments*periodic savings)

=$12,777.84 - (520*$20)

= $2377.84

So, Accumulated Amount Interest is $2377.84