Today a father deposits $12,500 in a bank that pays 8% annual interest. Additionally, make annual contributions due of $2,000 annually for 3 years. The fund is for your son to receive an annuity and pay for his studies for 5 years. If the child starts college after 4 years, how much is the value of the annuity? solve how well it is for an exam

To find the value of the annuity, we need to calculate the future value of the initial deposit and the annual contributions.

Step 1: Calculate the future value of the initial deposit. The formula for calculating the future value compounded annually is:

FV = PV(1+r)^n

Where:
FV = Future value
PV = Present value (initial deposit)
r = Interest rate
n = Number of years

In this case, the present value (PV) is $12,500, the interest rate (r) is 8%, and the number of years (n) is 4 since the child starts college after 4 years.

FV = 12,500(1+0.08)^4
FV = 12,500(1.08)^4
FV \approx 12,500 \times 1.36049
FV \approx 17,006.13

Step 2: Calculate the future value of the annual contributions. Since the annual contributions are received for 3 years, we can calculate the future value using the formula:

FV = P [(1 + r)^n - 1] / r

Where:
FV = Future value of the annuity
P = Annual contribution
r = Interest rate
n = Number of years

In this case, the annual contribution (P) is $2,000, the interest rate (r) is 8%, and the number of years (n) is 3.

FV = 2,000 [(1 + 0.08)^3 - 1] / 0.08
FV = 2,000 [(1.08)^3 - 1] / 0.08
FV = 2,000 [1.259712 - 1] / 0.08
FV = 2,000 \times 0.259712 / 0.08
FV\approx6,492.8

Step 3: Add the future value of the initial deposit and the future value of the annual contributions to find the total future value of the annuity.

TotalFutureValue=17,006.13+6,492.8
TotalFutureValue\approx23,498.93

Answer: The value of the annuity is approximately $23,498.93.