Question

You just won $17,500 and deposited your winnings into an account that pays 6.7 percent interest, compounded annually. How long will you have to wait until your winnings are worth $50,000

Answer 1

Answer:

16.20 years

Explanation:

In order to calculate this, we use the future value (FV) formula as follows:

FV = PV × (1 + r)^n …………………………….. (1)

Where;

FV = Future value of the winnings = $50,000

PV = Present value of the winnings = $17,500

r = Interest rate = 6.7% = 0.067

n = number of years =?

Substituting the values above into equation (1) and solve for n, we have:

50,000 = 17,500 × (1 + 0.067)^n

50,000/17,500 = 1.067^n

2.85714285714286 = 1.067^n

Log linearizing and rearranging the above equation, we have:

n × ln1.067 = ln2.85714285714286

n × 0.0648509723196163 = 1.05082162483176

n = 1.05082162483176/0.0648509723196163 = 16.20 years

Therefore, you will have to wait for 16.20 years until your winnings are worth $50,000.