Answer:
a) $49,027.14
b) $54,501.67
Step-by-step explanation:
a) The account balance multiplier for interest rate r compounded n times per year for t years is ...
multiplier = (1 +r/n)^(nt)
For your numbers, r=.09, n=12, t=10, this is 2.45135708, so the account balance after 10 years will be ...
$20,000 × 2.45135708 ≈ $49,027.14
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b) All but $20,000 of the above balance is interest, so the amount invested for the second period is $29,027.14.
The multiplier for a continuously compounded interest rate r for t years is ...
multiplier = e^(rt)
For your numbers, r=.105 and t=6, so the multiplier is e^.63 ≈ 1.8776106 and the account balance for an investment of $29,027.14 will be ...
$29,027.14 × 1.8776106 ≈ $54,501.67
