Asked by Charmaine Butler on Apr 27, 2024
Verified
If you want to purchase an annuity providing an income of $2,000 at the end of each month for five years, how much will it cost if the purchase funds earn 18% compounded monthly?
A) $192,429.30
B) $78,760.54
C) $80,681.00
D) $4,886.44
E) $818.60
Compounded Monthly
Interest calculation method where the interest is added to the principal each month, and the total becomes the principal for the next calculation.
Annuity
An investment option that guarantees fixed payments over time to the holder, frequently adopted as a component of retirement planning.
Purchase Funds
Money allocated or spent for acquiring goods, services, or assets.
- Estimate the requisite sum to allocate for future economic goals using assorted financial tools.
- Compute the amounts of loans and formulate repayment strategies in relation to designated interest rates and durations.
Verified Answer
BS
Bayleigh SchadMay 02, 2024
Final Answer :
B
Explanation :
The cost of purchasing an annuity can be calculated using the present value formula for annuities. Given an annuity that pays $2,000 at the end of each month for five years (60 months) with an interest rate of 18% compounded monthly, the monthly interest rate is 18%/12 = 1.5%. Using the present value of an annuity formula: P=PMT×(1−(1+r)−nr)P = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)P=PMT×(r1−(1+r)−n) , where PMT = $2,000, r = 0.015 (1.5%), and n = 60, the calculation yields approximately $78,760.54.
Learning Objectives
- Estimate the requisite sum to allocate for future economic goals using assorted financial tools.
- Compute the amounts of loans and formulate repayment strategies in relation to designated interest rates and durations.