An initial deposit of $45,000 grows at an annual rate of 10% for 20 years. Compare the final balances resulting from continuous
compounding and annual compounding. (Round your answers to the nearest cent.)
1 answer:
Answer:
Annual: $302 737.50
Continuous: $332 507.52
Step-by-step explanation:
A. Compounded annually
The formula for <em>compound interest</em> is
A = P(1 + r)ⁿ
Data:
P = $45 000
r = 10 %
t = 20 yr
Calculations:
n = 20
A = 45 000(1+ 0.10)²⁰
= 45 000 × 1.10²⁰
= 45 000 × 6.727 499 95
= $302 737.50
B. Compounded continuously
The formula for <em>continuously compounded inerest</em> is



= 45 000 × 7.389 056 61
= $332 507.52
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