Find the Annual Interest Rate for Compounded Annually

D

On the BAII Plus, press 500 PV, 625 +/- FV, 0 PMT, 3 N, then CPT I/Y. On the HP12C, press 500 PV, 625 CHS FV, 0 PMT, 3 n, then press i.

To determine the annual interest rate that will cause an original deposit of $500 to grow to $625 after 3 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the future value of the deposit P = the initial deposit amount r = the annual interest rate (in decimal form) n = the number of times interest is compounded per year t = the number of years

In this case, we know the initial deposit is $500 (P = $500), the future value is $625 (A = $625), the number of years is 3 (t = 3), and the interest is compounded annually (n = 1).

Now we can plug in the values into the formula and solve for r:

$625 = $500(1 + r/1)^(1*3)

Simplifying further:

$625 = $500(1 + r)^3

Divide both sides by $500:

1.25 = (1 + r)^3

To isolate (1 + r), we can take the cube root of both sides:

(1 + r) = (1.25)^(1/3)

Using a calculator, we find that (1.25)^(1/3) is approximately 1.0905.

Subtracting 1 from both sides:

r = 1.0905 - 1

r = 0.0905

Finally, we convert the decimal form to a percentage:

r = 0.0905 * 100%

r ≈ 9.05%

Therefore, the annual interest rate, compounded annually, that will cause an original deposit of $500 to grow to $625 after 3 years is approximately 9.05%.

Among the answer choices provided, the closest option is B. 9.14%.