Multiple Choice
Janet takes out a loan of \$10,000 at an annual interest rate of 6ext{%}, to be repaid in equal monthly installments over 5 years. By the time Janet pays off her entire loan, how much total interest will she have paid?
118
views
10. Time Value of Money
Time Value of Money Equations
Multiple Choice
At an annual interest rate of 12.5\%, how many years will it take for an investment to triple in value if interest is compounded annually?
A
Approximately 9.4 years
B
Approximately 12.5 years
C
Approximately 6.2 years
D
Approximately 15.0 years
Verified step by step guidance1
Understand the formula for compound interest: \( A = P(1 + r)^t \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the time in years.
Since the investment triples in value, set \( A = 3P \). Substitute this into the formula to get \( 3P = P(1 + r)^t \). Simplify by dividing both sides by \( P \), resulting in \( 3 = (1 + r)^t \).
Convert the annual interest rate from a percentage to a decimal: \( r = 12.5\% = 0.125 \). Substitute \( r \) into the equation to get \( 3 = (1 + 0.125)^t \).
Take the natural logarithm (ln) of both sides to solve for \( t \): \( \ln(3) = t \cdot \ln(1.125) \). Rearrange to isolate \( t \): \( t = \frac{\ln(3)}{\ln(1.125)} \).
Use a calculator to compute \( \ln(3) \) and \( \ln(1.125) \), then divide the results to find \( t \), which represents the number of years it will take for the investment to triple in value.
Related Videos
Related Practice
