Question

Hannah would like to make an investment that will turn 8000 dollars into 31000 dollars in 4 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal?

Answer 1

This is the future value calculation.

Present value (PV) = $8,000

Future value (FV) = $31,000

Number of years (n) = 4

Number of quarter in a year (m) = 4

Rate of interest (r) =?

By the formula:

FV = PV (1 + (r/m))^(n × m)

31,000 = 8,000 (1 + (r/4))^(4 × 4)

(31,000/8,000) = (1 + (r/4))^16

3.875 = (1 + (r/m))^16

3.875 ^ (1/16) = (1 + (r/4)) ^(16/16)

3.875 ^0.0625 = 1 + (r/4)

1.088345 – 1 = (r/4)

0.088345 = (r/4)

r = 0.088345 × 4

= 0.35338

The yearly interest rate is (r × 100 = 0.35338 × 100 =) 35.338%