The table lists interest rates on long-term investments (based on 10-year government bonds)in several countries in 2004-2005. Assuming that you invest $11,000 in Japan, how long (to the nearest year)must you wait before your investment is worth $17,000 if the interest is compounded annually? Country U.S. Japan Canada Yield 5.3% 1.5% 5.2%
A)29 years
B)24 years
C)25 years
D)32 years
E)30 years

Question

Quizplus · Accepted Answer

To find the number of years required for an investment to grow from $11,000 to $17,000 with an annual interest rate of 1.5% (Japan's rate), we use the formula for compound interest: $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount ($11,000), $r$ is the annual interest rate (1.5% or 0.015), and $t$ is the time the money is invested for in years.Rearranging the formula to solve for $t$, we get:$$17000 = 11000(1 + 0.015)^t$$Dividing both sides by 11000:$$1.54545 = (1.015)^t$$Taking the natural logarithm of both sides to solve for $t$:$$ln(1.54545) = t \cdot ln(1.015)$$$$t = \frac{ln(1.54545)}{ln(1.015)}$$$$t ≈ 29$$Therefore, it takes approximately 29 years for the investment to grow to $17,000.

The Table Lists Interest Rates on Long-Term Investments (Based on 10-Year