Question

Emma is saving money for college. She has $800 and wants to deposit it into 2 different savings accounts. She decides to deposit $500.00 into an account, Account I, which earns 2.5% annual simple interest. She will then deposit $300 into an account, Account II, which earns 2 1 4 % interest compounded annually. If Emma makes no other deposits or withdrawals, what is the total amount of money she will have at the end of 3 years?

Answer 1

Answer:

The amount would be $ 858.21

Step-by-step explanation:

Given,

In first account,

Deposited amount, $P_1$ = $ 500,

Annual simple interest, $r_1$ = 2.5%,

Number of years, $t_1$ = 3 years,

So, the amount after 3 years,

$A_1 = P_1 + \frac{P_1\times r_1\times t_1}{100}$

$A_1 = 500 + \frac{500\times 2.5\times 3}{100}$

$A_1 = 500 + \frac{3750}{100}$

$A_1 = 500 + 37.50$

$A_1 = 537.5$

In second account,

Deposited amount, $P_2$ = $ 300,

Annual compound interest, $r_2$ = 2.25%, ( ∵ $2\frac{1}{4}=2.25$ )

Number of years, $t_2$ = 3 years,

So, the amount after 3 years,

$A_2 = P_2(1 + \frac{r_2}{100})^{t_2}$

$A_2= 300(1+\frac{2.25}{100})^3$

$A_2 = 300(1+0.0225)^3$

$A_2 = 300(1.0225)^3$

$A_2 = 320.71$

Hence, the total amount,

$A=A_1 + A_2 = 537.5 + 320.71 = \ 858.21$