Direct answer:a) The balance at the end of the period is $1439.57. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.).b) The interest earned is $318.57. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.).c) The effective rate of interest is 11.21%. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)An amount of $1100.00 earns $500.00 interest in two years, four months. What is the effective annual rate of interest if it compounds monthly?The effective annual rate of interest as a percent is 8.00%. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)
The formula for calculating compound interest is given by,WhereA is the final amount,P is the principal,r is the rate of interest,n is the number of times interest is compounded in a year,t is the number of yearsJessica made a deposit of $1121.00 into a bank account that earns interest at 10.7% compounded monthly. The deposit earns interest at that rate for three years.The principal is $1121.00The rate of interest per month is $\frac{10.7}{12}=0.8917$The number of times interest is compounded in a year is 12 times.The number of years is 3 years.So,The balance at the end of the period is, $A=1121\left(1+\frac{0.107}{12}\right)^{12\times3}$ = $1121\times1.107005^{36}=1439.57$Therefore, the balance at the end of the period is $1439.57$. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)The interest earned is the difference between the amount and the principal. So, the interest earned is,$S=A-P=1439.57-1121=318.57$Therefore, the interest earned is $318.57$. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)The effective rate of interest formula is given by,$r_{eff}=\left(1+\frac{r}{n}\right)^n-1$Here,r is the rate of interest per year,n is the number of times the interest is compounded in a year.So, the effective rate of interest is,$r_{eff}=\left(1+\frac{0.107}{12}\right)^{12}-1=0.112069-1=-0.887931$Converting this into a percentage, we get,$r_{eff}=0.112069\times100-100=-11.7931\%$So, the effective rate of interest is -11.7931%. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)An amount of $1100.00 earns $500.00 interest in two years, four months. What is the effective annual rate of interest if it compounds monthly?The formula for calculating compound interest is given by,$A=P\left(1+\frac{r}{n}\right)^{nt}$WhereA is the final amount,P is the principal,r is the rate of interest,n is the number of times interest is compounded in a year,t is the number of yearsGiven that, the principal is $P=1100.00$The interest earned is $S=500.00$The number of times interest is compounded in a year is 12 times.The number of years is 2 years and 4 months = $\frac{28}{12}=2.33$ yearsSo, using the formula, we can find the rate of interest per year,r$=\left(n\sqrt[t]{\frac{A}{P}}-1\right)\times100$Here, A is the final amount which is $P+S=1100+500=1600$So, r = $\left(12\sqrt[2.33]{\frac{1600}{1100}}-1\right)\times100$ = $(12\times1.119921-1)\times100=8.00\%$Therefore, the effective annual rate of interest as a percent is 8.00%. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)