Asked by Ebani Thomas on Apr 23, 2024
Verified
What amount, invested today at 6% compounded monthly, will support perpetual monthly payments of $500? The first payment will be made one month from now.
A) $500,000
B) $400,000
C) $300,000
D) $200,000
E) $100,000
Compounded Monthly
Interest calculation method where interest accrued is added to the principal sum each month, leading to an increase in the subsequent month's interest calculation.
Interest Rate
The percentage at which interest is paid by a borrower for the use of money that they borrow from a lender.
- Determine the necessary initial investment to achieve desired future payments or perpetuities.
Verified Answer
RV
Ravuri Vishnu Vardhan Chowdary8 days ago
Final Answer :
E
Explanation :
To find the principal amount that can support perpetual monthly payments of $500 at an interest rate of 6% compounded monthly, we use the formula for the present value of a perpetuity: PV=PMTrPV = \frac{PMT}{r}PV=rPMT , where PMT is the monthly payment and r is the monthly interest rate. The annual interest rate is 6%, so the monthly interest rate is 0.06/12=0.0050.06/12 = 0.0050.06/12=0.005 . Plugging in the values, we get PV=5000.005=100,000PV = \frac{500}{0.005} = 100,000PV=0.005500=100,000 . Therefore, an investment of $100,000 is needed.
Learning Objectives
- Determine the necessary initial investment to achieve desired future payments or perpetuities.
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