What annual interest rate, compounded annually, will cause a deposit of $850 to become $1,475 in 10 years?
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A. B. C. D. E.A
On the BAII Plus, press 10 N, 850 PV, 1475 +/- FV, 0 PMT, CPT I/Y. On the HP12C, press 10 n, 850 PV, 1475 CHS FV, 0 PMT, i. Make sure that the BAII Plus has the P/Y value set to 1.
To find the annual interest rate that will cause a deposit of $850 to grow to $1,475 in 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = the future value of the deposit ($1,475) P = the initial deposit ($850) r = the annual interest rate (unknown) n = the number of times the interest is compounded per year (compounded annually, so n = 1) t = the number of years (10)
Substituting the given values into the formula, we get:
1,475 = 850(1 + r/1)^(1*10)
Simplifying further:
1,475/850 = (1 + r)^10
1.735 = (1 + r)^10
To solve for r, we need to take the 10th root of both sides:
(1 + r) = 1.735^(1/10)
(1 + r) ≈ 1.0770
Now, subtracting 1 from both sides:
r ≈ 1.0770 - 1
r ≈ 0.0770
Converting the decimal to a percentage:
r ≈ 7.70%
Among the given answer choices, the closest option is C. 7.88%.