Concept explainers
Funding an Annuity A 55-year-old man deposits $50,000 to fund an annuity with an insurance company. The money will be invested at 8% per year, compounded semiannually. He is to draw semiannual payments until he reaches age 65. What is the amount of each payment ?
To find: The amount of each payment.
Answer to Problem 14E
The amount of each payment is $3,679.09.
Explanation of Solution
Given:
Present Value = $50,000
Interest Rate = 8% per year (or 4% semiannually)
Number of Payments = 10 years (or 20 months)
Formula:
Here,
Ap = Present Value
R = Periodic Payment
i = Interest Rate
n = Number of Years/Payments
Annuity: An annuity is a form of financial contract that are typically used for retirement plans by the insurance companies which assures guaranteed payment to the insurer. It is paid by the insurance company for a certain period of time or on lifetime basis.
Calculation:
The amount of each payment is calculated by multiplying the present value with interest rate and the result is divided by 1 minus, 1 plus interest rate to the power minus number of years.
Therefore, the amount of each payment is $3,679.09.
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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