Solve the problem. Round to the nearest cent as needed.
-An actuary for a pension fund need to have $14.6 million grow to $22 million in 6 years. What interest rate compounded annually does he need for this investment to growth as specified. Round your answer to the
Nearest hundredth of a percent.
A) 0.07%
B) 7%
C) 7.7%
D) 7.07%

Question

Quizplus · Accepted Answer

We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the ending amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the time in years. We know P = $14.6 million, A = $22 million, n = 1 (compounded annually), and t = 6 years. We can solve for r:

$22 million = $14.6 million (1+r/1)^(1*6)
(22/14.6) = (1+r)^6
1.5068 = (1+r)^6
6(log(1+r)) = log(1.5068)
log(1+r) = log(1.5068)/6
1+r = 1.0707
r = 0.0707 or 7.07%

Therefore, the best choice is D. We can use the formula A=P(1+r/n)^(nt) where A=$22 million, P=$14.6 million, n=1 (compounded annually), t=6 years, and solve for r (interest rate).
$22 million = $14.6 million(1+r/1)^(1*6)
(22/14.6) = (1+r)^6
1.50684932 = (1+r)^6
Taking the sixth root of both sides:
(1+r) = 1.07069998
r = 0.07069998 or 7.07% (rounded to nearest hundredth of a percent)

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