Question

Compound Interest Application

Compound interest is given by the formula A = P ( 1 + r ) t . Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r , expressed as a decimal.

Wyatt is investing money into a savings account that pays 2% interest compounded annually, and plans to leave it there for 15 years. Determine what Wyatt needs to deposit now in order to have a balance of $40,000 in his savings account after 15 years.

Wyatt will have to invest $___________ now in order to have a balance of $40,000 in his savings account after 15 years. Round your answer UP to the nearest dollar.

Answer 1

$29,721

Explanation:

We have been given that Wyatt is investing money into a savings account that pays 2% interest compounded annually, and plans to leave it there for 15 years. We are asked to find the amount deposited by Wyatt in order to have a balance of $40,000 in his savings account after 15 years.

We will use compound interest formula to solve our given problem.

`A=P(1+(r)/(n))^(nT)`, where,

A = Final amount after T years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

T = Time in years.

Let us convert our given interest rate in decimal form.

`2\%=(2)/(100)=0.02`

Upon substituting our given values in compound interest formula, we will get:

`\$40,000=P(1+(0.02)/(1))^(1*15)`

`\$40,000=P(1+0.02)^(15)`

`\$40,000=P(1.02)^(15)`

`\$40,000=P* 1.3458683383241296`

Switch sides:

`P* 1.3458683383241296=\$40,000`

`(P* 1.3458683383241296)/( 1.3458683383241296)=(\$40,000)/(1.3458683383241296)`

`P=\$29,720.5891995`

Upon rounding our answer to nearest dollar, we will get:

`P\approx \$29,721`

Therefore, Wyatt will have to invest $29,721 now in order to have a balance of $40,000 in his savings account after 15 years.