Question

Suppose I have the choice of investing $25000 in two different accounts:

Acct.1: 4.5% compounded semi-annually

Acct 2: 3.75% compounded monthly

What is the future value of each account? In other words, what will be the final compounded amount in each account after 6 years (assuming no additional deposits or withdrawals)? How much interest does each account produce? Please show your work.

Answer 1

- You want to Invest $25,000 in two different accounts, Calculating the Future value of each account after 6 years:-

Acct.1: 4.5% compounded semi-annually

Calculating the Future value of Account 1 after 6 years:-

Future value = Invested amount*(1+r)^n

Where, Invested amount = $25,000

r = Periodic Interest rate = 4.5%/2 = 2.25%

n= no of periods = 6 years*2 = 12

Future value = $25,000*(1+0.0225)^12

Future value = $25,000*1.30604998989

Future value at the end of year 6= 32,651.25

- Interest earned by account = Future Vaue - Invested amount

= $32,651.25 - $25,000

Interest earned by account = $7,651.25

Acct 2: 3.75% compounded monthly

Calculating the Future value of Account 2 after 6 years:-

Future value = Invested amount*(1+r)^n

Where, Invested amount = $25,000

r = Periodic Interest rate = 3.75%/12 =0.3125%

n= no of periods = 6 years*12 = 72

Future value = $25,000*(1+0.003125)^72

Future value = $25,000*1.25188343863

Future value at the end of year 6= 31,297.09

- Interest earned by account = Future Vaue - Invested amount

= $31,297.09 - $25,000

Interest earned by account = $6,297.09

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