Question

Ann and Tom went to establish a fund for their grandson's college education what lump sum must they deposit at a 10% annual interest rate compounded quarterly in order to have $30,000 in the fund at the end of 15 years?

Answer 1

We will have the following:

*First: We have the expression:

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

Here "A" is the final amount, "P" is the intitial principal balance, "r" is the interest rate, "n" is the number of times interest applied per time period & "t" is the number of time periods.

*Second: We determine the values given:

A = $30 000

r = 0.1

n = 4

t = 15

*Third: We replace in the expression and solve for P:

`30000=P(1+(0.1)/(4))^((4)(15))\Rightarrow30000=P((41)/(40))^((60))`
`\Rightarrow P=(30000)/(((41)/(40))^((60)))\Rightarrow P=6818.507636\ldots`
`\Rightarrow P\approx6818.5`

So, Ann and Tom would need to deposit approximately $6818.5 at the begining.