Multiple Choice
If you earn an annual interest rate of 6.9\% compounded annually, approximately how many years will it take to double your savings?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the present value of a \$600 annuity payment received at the end of each year for 4 years, if the interest rate is 6\% per year?
A
\$2,122.56
B
\$2,500.00
C
\$2,000.00
D
\$2,400.00
Verified step by step guidance1
Step 1: Understand the concept of present value of an annuity. Present value is the current worth of a series of future payments, discounted at a specific interest rate. An annuity is a series of equal payments made at regular intervals.
Step 2: Use the Present Value of an Ordinary Annuity formula: \( PV = P \times \frac{1 - (1 + r)^{-n}}{r} \), where \( P \) is the annuity payment, \( r \) is the interest rate per period, and \( n \) is the number of periods.
Step 3: Substitute the given values into the formula: \( P = 600 \), \( r = 0.06 \), and \( n = 4 \). The formula becomes \( PV = 600 \times \frac{1 - (1 + 0.06)^{-4}}{0.06} \).
Step 4: Calculate the term \( (1 + r)^{-n} \). This involves raising \( (1 + 0.06) \) to the power of \( -4 \). Then subtract this value from 1.
Step 5: Divide the result from Step 4 by \( r \) (0.06), and multiply the quotient by \( P \) (600) to find the present value of the annuity.
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