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 age 8 if they are allowed to have $20,000 on entering collage 10 years later, assuming 6% interest compounded semiannually?

Answer 1

ANSWER

$11,073.52

EXPLANATION

The compound interest formula is,

$A=P\mleft(1+\frac{r}{n}\mright)^{nt}$

Where:

• P is the initial amount - this is what we have to find

,

• A is the amount after t years, $20,000

,

• r is the interest rate, 0.06

,

• n is the number of times the interest is compounded per year, 2 (semiannually)

,

• t is the time in years, 10

Replace this information in the equation,

$20000=P\cdot\mleft(1+\frac{0.06}{2}\mright)^{2\cdot10}$

And solve for P,

$P=\frac{20000}{(1+\frac{0.06}{2})^{20}}=\frac{20000}{(1+0.03)^{20}}=\frac{20000}{1.03^{20}}\approx11073.52$

Hence, she must give $11,073.52 to each grandchild at the age of 8.