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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
Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
We will simplify this first a bit by dividing 2000 by 1150 to get
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.