Question

Parents wish to have $100,00 available for a child’s education. If the child is now 9 years old, how much money must be set aside at 6% compounded semiannually to meet their financial goal when the child is 18.

The amount that should be set aside is $____. (Round up to the nearest dollar.)

Answer 1

$58,739.46 so $58,739

Explanation:

I suspect you want $100,000 not $10000

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

A = final amount

P = initial principal

r = interest rate

n = number of times the interest is applied per time period

t = number of time periods elapsed

number of time periods is 18-9 = 9

semiannual 2 makes n = 2

A = 100,000

P = ????

r = 0.06

n = 2

t = 2

I used to finance calculator app to find P = 58739.46

and double checked by using the formula to find A

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

= 58739( 1 + 0.06/2)^(2(9))

= 58739.46( 1.03)^18

= 99999.9987

OR

A = P(1 + r/t)^nt solve for P

P = A/[(1 + r/t)^nt]

= 10000/[(1 + 0.06/2)^(2(9))]

= 100000 / [1.03^18]

= $58,739.46