Question

Suppose a young couple deposits $600 at the end of each quarter in an account that earns 6.8%, compounded quarterly, for a period of 2 years. After the 2 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 2 years in the account and continue to contribute $200 at the end of each quarter for the next 18 1/2 years, how much will they have in the account (to help with their child's college expenses)? (Round your answer to the nearest cent.)

Answer 1

- Periodic Quarterly deposit by Young couple for 2 years= $600

Calculating the Future Value at the end of year 2:-

Where, C= Periodic Payments = $600

r = Periodic Interest rate = 6.8%/4 = 1.7%

n= no of periods = 2 years*4 = 8

Future Value at the end of year 2 is $5095.52

- After 2 years, she made Periodic Quarterly deposit of $200 at the end of each quarter for the next 18 1/2 years(or 18.5 years).

Other than Quartery deposit they kept the Future Value at the end of year 2 in the account and the amount earned interest for the next 18.5 years

Calculating the Future Value at the end :-

Where, C= Periodic Payments = $200

r = Periodic Interest rate = 6.8%/4 = 1.7%

n= no of periods = 18.5 years*4 = 74

Value 2 = Future Value at the end of year 2 = $5095.52

Future value = $29,192.62 + $17,739.40

Future Value = $46,932.02

So, the amount they will have at the end is $46,932.02

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