Question

1] A newborn child receives a $20000 gift towards her tertiary education from her grandparents who insisted the gift should be put in investment for 18 years by the baby’s parents. The highest rate offered was 7%. Parents of the baby opted for the investment to be compounded quarterly.

i. What is the compound interest on the investment

ii. How much is the investment worth.

Answer 1

1.The compound interest on the investment

Compound interest = $=P[(1+i)^n-1]$

where the principal amount (P) = 20000

the nominal interest rate (i) = $​ \frac{0.07}{4}$

number of compounding periods (n) $=18*4=72$

Compound interest = $20000[(1+ ​ \frac{0.07}{4})$⁷² -1]

$=20000*2.487209897$

$= 49744.19794$

The compound interest on the investment is approximately $49744.20

2.The investment worth

The investment worth (A) = P + I

where I is the compound interest

A$= 20000+49744.20$

$=69744.20$

The investment is worth approximately $69744.20