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: 858.21

This is the total of the amount of money she will have in 3 years.

Answer 2

The amount would be $ 858.21

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 + (P_1* r_1* t_1)/(100)`

`A_1 = 500 + (500* 2.5* 3)/(100)`

`A_1 = 500 + (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(1)/(4)=2.25` )

Number of years,
`t_2` = 3 years,

So, the amount after 3 years,

`A_2 = P_2(1 + (r_2)/(100))^(t_2)`

`A_2= 300(1+(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`