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

$11,073.52

Step-by-step explanation

The compound interest formula is,

`A=P\mleft(1+(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+(0.06)/(2)\mright)^(2\cdot10)`

And solve for P,

`P=(20000)/((1+(0.06)/(2))^(20))=(20000)/((1+0.03)^(20))=(20000)/(1.03^(20))\approx11073.52`

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