What annual interest rate, compounded annually, will cause an original deposit of $400 to grow to $725, after 7 years?
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A. B. C. D. E.Explanation
On the BAII Plus, press 400 PV, 725 +/- FV, 0 PMT, 7 N, then CPT I/Y. On the HP12C, press 400 PV, 725 CHS FV, 0 PMT, 7 n, then press i. Make sure the BAII
Plus has the P/Y value set to 1.
To solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = the future value of the investment P = the principal (original deposit) r = annual interest rate (in decimal form) n = number of times the interest is compounded per year t = number of years
In this case, we have: P = $400 (original deposit) A = $725 (desired future value) t = 7 years
We need to find the annual interest rate, so we set up the equation and solve for r.
$725 = $400(1 + r/1)^(1*7)
Now, let's simplify and solve the equation step by step:
$725/$400 = (1 + r)^7
1.8125 = (1 + r)^7
To isolate the (1 + r) term, we take the seventh root of both sides:
(1 + r) = (1.8125)^(1/7)
(1 + r) ≈ 1.0887
Subtracting 1 from both sides, we get:
r ≈ 0.0887
To convert the decimal to a percentage, multiply by 100:
r ≈ 8.87%
Therefore, the correct answer is E. 8.87%.