Answer:
The size of the fund at the end of 7 years is $483.110
Explanation:
Number of quarters = 4
We are given that the nominal rate of discount convertible quarterly is 4/41
Discount rate in each quarter =[tex]\frac{\frac{4}{41}}{4} = \frac{1}{41}.[/tex]
Let A is the value after discount and X is the original value:
[tex]A = X - X(\frac{1}{41}) \\A=X(1 - \frac{1}{41}) \\A=\frac{40}{41}X\\X = \frac{41}{40}A[/tex]
Now To calculate the value after 7 years we need to multiply each value by the interest raised to the correct power.
[tex]A=100 \times 1.025^1 \times \frac{41}{40}^{(7-1) \times 4}+100 \times 1.025^3 \times \frac{41}{40}^{(7-3) \times 4}+100 \times 1.025^5 \times \frac{41}{40}^{(7-5) \times 4}[/tex]
A=483.110
Hence the size of the fund at the end of 7 years is $483.110
