9514 1404 393
Answer:
B. Between 9% and 9.9%
Step-by-step explanation:
The equation for the sum of a series of monthly payments P earning interest rate r compounded monthly for t years is given by ...
A = P((1 +r/12)^(12t) -1)/(r/12)
The number of years in this case is ...
70 -18 = 52
We want to find r such that ...
1,000,000 = 50·12((1 +r/12)^(12·52) -1)/r
10,000/6 = ((1 +r/12)^624 -1)/r
We can try some values for r to see what may work.
r = 9%
((1 +.09/12)^624 -1)/.09 = 1165.60 . . . not quite enough
r = 10%
((1 +0.10/12)^624 -1)/0.10 = 176408 . . . > 1666.67
The required interest rate will be between 9% and 10%, option B.
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In general, finding the exact interest rate is an iterative process. A financial calculator can do it for you. The result is near 9.86%. The graph shows a solution using a graphing calculator.
