 If $25,000 is invested for 15 years compounded quarterly and grows to$52,680. Find the interest rate to the nearest percent. Jaya Legge 2021-06-07 Answered
If $25,000 is invested for 15 years compounded quarterly and grows to$52,680. Find the interest rate to the nearest percent.

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Clelioo

Use the compound interest formula: $$\displaystyle{A}={P}{\left({1}+\frac{{r}}{{n}}\right)}^{{n}}{t}$$
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: $$\displaystyle{52680}={25000}{\left({1}+\frac{{r}}{{4}}\right)}^{{4}}{\left({15}\right)}$$
$$\displaystyle{52680}={25000}{\left({1}+\frac{{r}}{{4}}\right)}^{{60}}$$
Divide both sides by 25000: $$\displaystyle{2.1072}={\left({1}+\frac{{r}}{{4}}\right)}^{{60}}$$
Raise both sides by $$\displaystyle\frac{{1}}{{60}}$$: $$\displaystyle{2.1072}={1}+\frac{{r}}{{4}}$$
Subtract 1 from both sides: $$\displaystyle{\left(\frac{{2.1072}^{{1}}}{{60}}\right)}-{1}=\frac{{r}}{{4}}$$
Multiply both sides by 4: $$4((2.1072^1/60)-1)=r r=0.05->5%$$

Not exactly what you’re looking for? content_user

Answer is given below (on video)