Question

Suppose that $65,000 is invested at 6 % interest, compounded quarterly.

a) Find the function for the amount to which the investment grows after t years.
b) Find the amount of money in the account at t = 0, 4, 8, and 10 years.

Answer 1

a) A(t) = 65000(1.01625^(4t))

b) 0 years: $65,000; 4 years: $84,124.46;

8 years: $108,875.77; 10 years: $123,861.32

Explanation:

You want a function for the amount of a $65,000 investment after t years if it earns interest at 6.5% compounded quarterly, and you want to find the value after 0, 4, 8, and 10 years.

a) Compound interest

The compound interest formula is ...

A = P(1 +r/n)^(nt)

amount of principal P earning rate r compounded n times per year for t years.

For the given values, the function for the amount is ...

A(t) = 65000(1 +0.065/4)^(4t)

A(t) = 65000(1.01625^(4t))

b) Account value

The value of the account will be ...

• 0 years: $65,000
• 4 years: $84,124.46
• 8 years: $108,875.77
• 10 years: $123,861.32

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