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?
800+(500(0.025) + 300(0.0225))*3
2 1/4^^
this is due soon pls help
To find the total amount of money Emma will have at the end of 3 years, we need to calculate the future value of each account and then add them together.
Let's start with Account I, which earns 2.5% annual simple interest. The formula for simple interest is:
Future Value (FV) = Principal (P) × (1 + (r × t))
Where:
- P is the principal amount (the initial deposit)
- r is the annual interest rate (expressed as a decimal)
- t is the time period in years
For Account I:
- Principal (P) = $500.00
- Annual interest rate (r) = 2.5% = 0.025 (as a decimal)
- Time period (t) = 3 years
Calculating the future value of Account I:
FV of Account I = $500.00 × (1 + (0.025 × 3))
FV of Account I = $500.00 × (1 + 0.075)
FV of Account I = $500.00 × 1.075
FV of Account I = $537.50
Now let's move on to Account II, which earns 2 1/4% interest compounded annually. The formula for compound interest is:
Future Value (FV) = Principal (P) × (1 + r)^t
Where:
- P is the principal amount (the initial deposit)
- r is the annual interest rate (expressed as a decimal)
- t is the time period in years
For Account II:
- Principal (P) = $300.00
- Annual interest rate (r) = 2 1/4% = 2.25% = 0.0225 (as a decimal)
- Time period (t) = 3 years
Calculating the future value of Account II:
FV of Account II = $300.00 × (1 + 0.0225)^3
FV of Account II = $300.00 × (1.0225)^3
FV of Account II = $300.00 × 1.067779…
Now, let's calculate the total amount of money Emma will have at the end of 3 years by adding the future values of both accounts together:
Total amount = FV of Account I + FV of Account II
Total amount = $537.50 + ($300.00 × 1.067779…)
Total amount = $537.50 + $320.33…
Total amount = $857.83…
Therefore, at the end of 3 years, Emma will have approximately $857.83 in total.