Question

What annual interest rate do you need for an investment to be worth $4,345.47 four years in the future with semi-annual compounding if you deposit $3,300 today? Please show ALL work with finance formulas.

Answer 1

For compound interest, we have

A = P*(1+r)^n

Where, A = Amount received = $4,345.47

P = principal = $3,300

r = rate of interest compounded semi annually

n = period = 4 years = 4*2 periods (as semi annual compounding indicated 2 periods per year) = 8 periods

Thus,

4535.47 = 3300* (1+r)^8

Thus,

(1+r)^8 = (4535.47/3300)

1+r = (4535.47/3300)^1/8

r = (4535.47/3300)^1/8 - 1

Thus, r = 0.04055

As this is semi annual compounding, annual interest rate = 2*0.04055 = 0.0811

= 8.11%