Question

Parents agree to invest $700 (at 12%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the dean's list during his 4 years in college. If he makes the dean's list in each of the 8 semesters, how much money will his parents have to give him when he graduates

Answer 1

$6,928.22 (approx)

Step-by-step explanation:

Given:

Periodic Payment = $700

Interest rate = 12% = 12% / 2 = 6% semi-annual = 6 / 100 = 0.06

Number of payment = 4 year = 4 × 2 = 8

Future value = ?

Computation of future value:

Future value :

`Future \ value = Pmt[((1+r)^n-1)/(r) ]\\\\Future \ value = 700[((1+0.06)^(8)-1)/(0.06) ]\\\\Future \ value = 700[((1.06)^(8)-1)/(0.06) ]\\\\Future \ value = 700[(1.593848-1)/(0.06) ]\\\\Future \ value = 700[(0.593848)/(0.06) ]\\\\Future \ value = 700[9.897466783]\\\\Future \ value = 6,928.22748\\\\`

Therefore, total amount to gave is $6,928.22