Respuesta :
We have been given that Mr. Jimenez has $10,000 to put into two different savings accounts. Mr. Jimenez will deposit $4,000 into Account I, which earns 4.5% annual simple interest. He will deposit $6,000 into Account II, which earns 4% interest compounded annually.
We are asked to find the total balance of these accounts at the end of 2 years.
We will use compound interest formula and simple interest formula to solve our given problem.
Simple interest formula:
[tex]A=P(1+rt)[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form.
[tex]4.5\%=\frac{4.5}{100}=0.045[/tex]
Let us find amount earned in 2 years at simple interest.
[tex]A=\$4,000(1+0.045\cdot 2)[/tex]
[tex]A=\$4,000(1+0.09)[/tex]
[tex]A=\$4,000(1.09)[/tex]
[tex]A=\$4360[/tex]
Now we will use compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where, n represents number of times interest compounded per year.
[tex]4\%=\frac{4}{100}=0.04[/tex]
[tex]A=\$6,000(1+\frac{0.04}{1})^{1\cdot 2}[/tex]
[tex]A=\$6,000(1+0.04)^2[/tex]
[tex]A=\$6,000(1.0816)[/tex]
[tex]A=\$6489.60[/tex]
Let us add both amounts.
[tex]\$6489.60+\$4360=\$10,849.60[/tex]
Therefore, the total balance of these accounts at the end of two years will be $10,849.60.
