At what annual interest rate must 137000 be invested so that it will grow to be 475009 in 14 years

Question

ScanSolve AI Tutor · Accepted Answer

Let's determine the annual interest rate.

Identify the formula for Future Value (FV).
The formula to find the future value of a present sum is:
$FV = PV \times (1 + r)^n$
Where:
FV = Future Value ( $475,009) PV = Present Value ($ 137,000) r = Annual interest rate (what we need to find)
n = Number of years (14)
Substitute the given values into the formula.
$475,009 = 137,000 \times (1 + r)^{14}$
Isolate the term $(1 + r)^{14}$ .
Divide both sides by 137,000:
$\frac{475,009}{137,000} = (1 + r)^{14}$ $3.467218978 \approx (1 + r)^{14}$
Solve for $(1 + r)$ by taking the 14th root of both sides.
$(1 + r) = (3.467218978)^{\frac{1}{14}}$ $(1 + r) \approx 1.09300$
Solve for $r$ .
$r = 1.09300 - 1$ $r = 0.09300$
Convert the interest rate to a percentage.
$r = 0.09300 \times 100\%$ $r = 9.30\%$
State the final answer.
The annual interest rate must be approximately 9.30%.

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