Multiple Choice
Which three variables primarily determine the amount of interest a person could earn from a savings account, according to the time value of money equations?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If you want to have \$1,000,000 saved at retirement in 30 years and you can earn an annual interest rate of 6\% compounded monthly, how much must you deposit at the end of each month? (Assume payments are made at the end of each period.)
A
Approximately \$2,778 per month
B
Approximately \$1,074 per month
C
Approximately \$1,667 per month
D
Approximately \$555 per month
Verified step by step guidance1
Step 1: Identify the type of problem. This is a future value of an ordinary annuity problem, where you want to determine the monthly payment required to reach a specific future value.
Step 2: Use the formula for the future value of an ordinary annuity: FV = P * [(1 + r/n)^(n*t) - 1] / (r/n), where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Step 3: Substitute the known values into the formula: FV = \$1,000,000, r = 0.06 (6%), n = 12 (monthly compounding), and t = 30 years. Rearrange the formula to solve for P (the monthly payment).
Step 4: Calculate the effective interest rate per period (r/n) and the total number of periods (n*t). For this problem, r/n = 0.06/12 = 0.005, and n*t = 12 * 30 = 360.
Step 5: Solve for P by isolating it in the formula: P = FV / [(1 + r/n)^(n*t) - 1] / (r/n). Plug in the values and simplify step by step to find the monthly payment required.
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