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.
