Asked by Brett Lucas on Jun 24, 2024
Verified
Your aunt is about to retire,and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years,beginning a year from today.The going rate on such annuities is 6.25%.How much would it cost her to buy such an annuity today?
A) $770,963.15
B) $811,540.16
C) $852,117.17
D) $894,723.02
Annuity
A series of payments of a fixed amount for a specified number of periods.
Supplement Income
Additional income earned beyond the primary source of income, often used to meet extra expenses or save for future needs.
Going Rate
The current average or standard price for goods or services in a particular market or industry.
- Estimate the per annum withdrawals from capital invested, considering a stipulated rate of interest and period.
Verified Answer
CR
Christopher RepizoJun 25, 2024
Final Answer :
B
Explanation :
To calculate the cost of the annuity, we can use the present value of an annuity formula:
PV = PMT x [(1 - (1 / (1 + r)^n)) / r]
Where:
PMT = $65,000
r = 6.25% = 0.0625 (annual interest rate)
n = 25 (number of years)
Plugging in the numbers, we get:
PV = 65,000 x [(1 - (1 / (1 + 0.0625)^25)) / 0.0625]
PV = $811,540.16
Therefore, it would cost your aunt $811,540.16 to buy the annuity today. Option B is correct.
PV = PMT x [(1 - (1 / (1 + r)^n)) / r]
Where:
PMT = $65,000
r = 6.25% = 0.0625 (annual interest rate)
n = 25 (number of years)
Plugging in the numbers, we get:
PV = 65,000 x [(1 - (1 / (1 + 0.0625)^25)) / 0.0625]
PV = $811,540.16
Therefore, it would cost your aunt $811,540.16 to buy the annuity today. Option B is correct.
Learning Objectives
- Estimate the per annum withdrawals from capital invested, considering a stipulated rate of interest and period.