Question

Jaquin hopes to earn $700 in interest in 1.6 years time from $56,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds monthly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Answer 1

The annual rate of interest is 1.5441% and this can be determined by using the formula of compound interest and the given data.

Given :

• Jaquin hopes to earn $700 in interest in 1.6 years time from $56,000 that he has available to invest.
• To decide if it's feasible to do this by investing in an account that compounds monthly.

The formula of compound interest can be used to determine the annual rate of interest. The formula of compound interest is given by;

$\rm A = P(1+\dfrac{r}{n})^{nt}$

where A is the final amount, r is the interest rate, n is the number of times interest applied per time period, t is the number of time periods elapsed and P is the principal amount.

Now, substitute the known terms in the above formula.

$56700=56000(1+\dfrac{r}{12})^{12\times 1.6}$

Simplify the above expression.

$1.025=(1+\dfrac{r}{12})^{19.2}$

Take the log on both sides in the above expression.

$\rm log(1.025)=19.2\;log(1+\dfrac{r}{12})$

$\rm \dfrac{log(1.025)}{19.2}=\;log(1+\dfrac{r}{12})$

Further, simplify the above expression.

$\rm 0.0005585=log(1+\dfrac{r}{12})$

$\rm 1.001286 = 1+\dfrac{r}{12}$

$\rm 0.001286 = \dfrac{r}{12}$

0.015432 = r

To convert the value of 'r' in percentage multiply by 100.

r = 1.5441%

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https://brainly.com/question/22621039