Question

Mrs Lorez wants all of her grandchildren to go to college and decides to help financially. How much must she give to each child at birth if they are to have $20,000 on entering college 18 years later, assuming 6% interest compounded annually?

Answer 1

Given the compound Interest annually:

If the given principal is compounded annually, the amount after the time period at percent rate of interest, r, is given as: A = P(1 + r/100)t,

`A=P(1+(r)/(100))^t`

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 per year,

Then solve the equation for A

A = P(1 + r/n)nt

t = 18years

n= 1

`\begin{gathered} A=P(1+(r)/(100))^(nt) \\ A=20000(1+(6)/(100))^((1)(18)) \\ A=20000(1+0.06)^(18) \\ A=\text{ \$57,086.78} \end{gathered}`

Therefore Mrs Lorez must give each child $57,086.78 at birth