Find out the answer to "If $25,000 is invested for 15 years compounded..."

College
Algebra
College algebra
Transformations of functions

Jaya Legge

Answered question

2021-06-07

If $25,000 is invested for 15 years compounded quarterly and grows to $52,680. Find the interest rate to the nearest percent.

Answer & Explanation

Clelioo

Skilled2021-06-08Added 88 answers

Employing the compound interest formula: $A = P {(1 + \frac{r}{n})}^{n} t$
where A is the final value, P is the present value, r is the rate (in decimal form), and n is compounding times per year, and t is the time in years.
Substitute A=52680, P=25000, n=4 for quarterly, and t=15 then solve for r: $52680 = 25000 {(1 + \frac{r}{4})}^{4} (15)$
$52680 = 25000 {(1 + \frac{r}{4})}^{60}$
Divide both sides by 25000: $2.1072 = {(1 + \frac{r}{4})}^{60}$
Raise both sides by $\frac{1}{60}$ : $2.1072 = 1 + \frac{r}{4}$
Take 1 away from both sides: $(\frac{{2.1072}^{1}}{60}) - 1 = \frac{r}{4}$
Multiply both sides by 4: $4 (({2.1072}^{1} / 60) - 1) = r r = 0.05 - > 5$

Jeffrey Jordon

Expert2021-10-10Added 2605 answers

Answer is given below (on video)

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