Question

A child's grandparents wish to purchase a bond that matures in 18 years to be used for her college education. the bond pays 4% interest compounded semiannually. how much should they pay so that the bond will be worth $85000 at maturity

Answer 1

Answer: they should pay $41669

Explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited.

t represents the duration of the investment.

From the information given,

A = 85000

r = 4% = 4/100 = 0.04

n = 2 because it was compounded 2 times in a year.

t = 18 years

Therefore,

85000 = P(1 + 0.04/2)^2 × 18

85000 = P(1 + 0.02)^36

85000 = P(1.02)^36

85000 = 2.0399P

P = 85000/2.0399

P = 41669

Answer 2

P=$41,669.11779

They Should Pay $41,669.11779 so that the bond will be worth $85000 at maturity.

Explanation:

The formula we are going to use is:

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

Where:

A is the final Amount

P is the present Amount

r is the interest

n is time interest is compounded

t is the time in years

In our Case:

`85,000=P(1+(0.04)/(2))^(2*18)\\ 85,000=P(2.03988)\\P=\$41,669.11779`

They Should Pay $41,669.11779 so that the bond will be worth $85000 at maturity.