Question

Mr. Jiménez has $10,000 to put into two different savings accounts. · Mr. Jiménez 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. Mr. Jiménez will make no additional deposits or withdrawals. What will be the total balance of these accounts at the end of 2 years?

Answer 1

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:

$A=P(1+rt)$, where,

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form.

$4.5\%=\frac{4.5}{100}=0.045$

Let us find amount earned in 2 years at simple interest.

$A=\ 4,000(1+0.045\cdot 2)$

$A=\ 4,000(1+0.09)$

$A=\ 4,000(1.09)$

$A=\ 4360$

Now we will use compound interest formula.

$A=P(1+\frac{r}{n})^{nt}$, where, n represents number of times interest compounded per year.

$4\%=\frac{4}{100}=0.04$

$A=\ 6,000(1+\frac{0.04}{1})^{1\cdot 2}$

$A=\ 6,000(1+0.04)^2$

$A=\ 6,000(1.0816)$

$A=\ 6489.60$

Let us add both amounts.

$\ 6489.60+\ 4360=\ 10,849.60$

Therefore, the total balance of these accounts at the end of two years will be $10,849.60.