Question

Suppose a young couple deposits $500 at the end of each quarter in an account that earns 6.8%, compounded quarterly, for a period of 9 years. How much is in the account after the 9 years? (Round your answer to the nearest cent.)

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After the 9 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 9 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.)

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Answer 1

Question a:

P = Quarterly deposit = $500

n = 9*4 = 36 Quarters

r = Quarterly interest rate = 6.8%/4 = 1.7%

Account balance in 9 years = P * [(1+r)^n - 1] / r

= $500 * [(1+1.7%)^36 - 1] / 1.7%

= $500 * 0.83465456 / 0.017

= $24,548.6635

Therefore, account balance in 9 years is $24,548.66

Question b:

PV = Acccumulate balance $24,548.66

P = Quarterly deposit = $200

n = 18 1/2*4 = 74 Quarters

r = Quarterly interest rate = 6.8%/4 = 1.7%

Accumulated balance = [PV * (1+r)^n] + [P * [(1+r)^n - 1] / r]

= [$24,548.66 * (1+1.7%)^74 ] + [$200 * [(1+1.7%)^74 - 1] / 1.7%]

= [$24,548.66 * 3.48137268] + [$200 * 2.48137268 / 0.017]

= $85,463.0343 + $29,192.6198

= $114,655.654

Therefore, accumulated balance in the account is $114,655.65