Answer:
The person must leave the money for approximately 14.8 years.
Step-by-step explanation:
This can be calculated using the formula for calculating the future value as follows:
FV = PV * (1 + r)^n …………………………………. (1)
Where;
FV = Future value of the investment = 5600
PV = Present value of the investment = 3000
r = semiannual interest rate = 4.25% / 2 = 0.0425 / 2 = 0.02125
n = number of semiannuals = ?
Substitute the values into equation (1) and solve for n, we have:
5600 = 3000 * (1 + 0.02125)^n
5600 / 3000 = 1.02125^n
1.02125^n = 1.86666666666667
Loglinearizing both sides, we have:
nlog1.02125 = log1.86666666666667
n = log1.86666666666667 / log1.02125
n = 0.271066772286539 / 0.0091320695404719
n = 29.6829509548973
Since n is number of semiannuals, we divide the answer by 2 obtain the number of years as follows:
Number of years = 29.6829509548973 / 2 = 14.8414754774487
Rounding to the nearest tenth of year, we have:
Number of years = 14.8
Therefore, the person must leave the money for approximately 14.8 years.
