Solve the problem.
-Imelda inherited $20,000 and invested it in a mutual fund for two years. At the end of the two years, her investment had grown to $29,768. Find the annual interest rate that would yield this amount of money, if the
Interest is compounded annually. Use the formula,nnually. Use the formula, $$A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$$ to solve to solve.
A)0.22%
B)220%
C)22%
D)2.2%

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. In this case, since the interest is compounded annually, $n = 1$. We are given $A = 29,768$, $P = 20,000$, $n = 1$, and $t = 2$ years. Plugging these values into the formula gives:$$29,768 = 20,000(1 + \frac{r}{1})^{1*2}$$Simplifying, we get:$$29,768 = 20,000(1 + r)^2$$Dividing both sides by 20,000:$$1.4884 = (1 + r)^2$$Taking the square root of both sides:$$\sqrt{1.4884} = 1 + r$$$$1.22 = 1 + r$$Subtracting 1 from both sides:$$r = 0.22$$Since $r$ is expressed as a decimal, to find the percentage, we multiply by 100:$$r = 0.22 * 100 = 22\%$$Therefore, the annual interest rate is 22%.

Solve the Problem A=p(1+rn)ntA = p \left( 1 + \frac { r } { n } \right) ^ { n t }A=p(1+nr​)nt

Solve the Problem $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$