Question

Parents wish to have $90,000 available for a child's education. If the child is now 8 years old, how much money must be set aside at 5% compounded semiannually to meet their financial goal when the child is 18? Round up to the nearest dollar.

Answer 1

$55,000

Explanation:

We have been given that Parents wish to have 90000 available for a child's education. The child is now 8 years old. We are asked to find the amount of money that parents must set aside at 5% compounded semiannually to meet their financial goal when the child is 18.

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

, where,

A = Final amount

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

t = Time in years.

n=2 because it's compounded semiannually.

t=18-8 = 10

using formula for compound interest:

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

90000=P(1+0.05/2)^2×10

90000=P(1+0.025)^20

90000=P(1.025)^20

90000=P(1.63861644)

p=90000/1.63861644

P= $ 54,924.38486

to the nearest dollar P= $54,924

= $55,000 to the nearest dollar

Therefore, an amount of $$55,000 must be set aside to meet their financial goal when the child is 18.