Question
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
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Answer to a math question 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
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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.
Step 1: Calculate the future value of the initial deposit. The formula for calculating the future value compounded annually is:
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.
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:
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.
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.
Answer: The value of the annuity is approximately $23,498.93.
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