Question

The Tanners have received an $8000 gift from one of their parents to invest in their child’s college education. they estimate that they will need $20000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?

Answer 1

3.4%

Explanation:

For given problem:

P=8000

n=2*12=24 compounding perods

A=12000

A/P=(1+i)^24

12000/8000=(1+i)^24

1.5=(1+i)^24

take log of both sides

log1.5=24log(1+i)

log1.5/24=log(1+i)

.007337=log(1+i)

10^(.007337)=1+i

1+i=1.017

i=1.017-1=.017 (interest rate per compounding period)

annual interest rate=2*.017=.034 or 3.4%