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?
I have to show my work for this question, but I'm not sure how to do it.
To solve this question, we'll calculate the amount of money Emma will have in each account separately and then add the two amounts together to find the total.
1. Account I:
The formula for calculating simple interest is: I = P * r * t, where I is the interest, P is the principal amount, r is the rate of interest, and t is the time period.
Given:
Principal (P) = $500.00
Rate of interest (r) = 2.5% = 0.025 (as a decimal)
Time period (t) = 3 years
Using the formula, we can find the interest earned in Account I:
I = $500 * 0.025 * 3
I = $37.50
The amount in Account I after 3 years will be the sum of the principal and the interest earned:
Amount in Account I = P + I
Amount in Account I = $500 + $37.50
Amount in Account I = $537.50
2. Account II:
The formula for calculating compound interest is: A = P * (1 + r/n)^(n*t), where A is the total amount, P is the principal amount, r is the rate of interest, n is the number of times the interest is compounded per year, and t is the time period.
Given:
Principal (P) = $300.00
Rate of interest (r) = 2 1/4% = 0.0225 (as a decimal)
Number of times interest is compounded per year (n) = 1 (annually)
Time period (t) = 3 years
Using the formula, we can find the amount in Account II after 3 years:
A = $300*(1 + 0.0225/1)^(1*3)
A = $300*(1 + 0.0225)^3
A ≈ $300*(1.0225)^3
A ≈ $300*1.069489
Rounded to the nearest cent, the amount in Account II after 3 years will be approximately $320.85.
Finally, to find the total amount of money Emma will have at the end of 3 years, we add the amounts in both accounts:
Total amount = Amount in Account I + Amount in Account II
Total amount = $537.50 + $320.85
Total amount ≈ $858.35
Therefore, Emma will have approximately $858.35 at the end of 3 years.
To calculate the total amount of money Emma will have at the end of 3 years, we need to calculate the interest earned on both accounts and add it to the principal amount.
Let's start with Account I, which earns 2.5% annual simple interest. Simple interest is calculated as:
Interest = Principal * Rate * Time
Given:
Principal (P) = $500.00
Rate (R) = 2.5% = 0.025 (in decimal)
Time (T) = 3 years
Interest on Account I = P * R * T
= $500.00 * 0.025 * 3
= $37.50
So, Account I will earn $37.50 in interest over 3 years.
Now let's move on to Account II, which earns 2 1/4% interest compounded annually. Compounded interest is calculated using the formula:
A = P * (1 + (R / n))^(n * t)
Where:
A = Final amount
P = Principal
R = Interest rate (in decimal)
n = Number of compounding periods per year
t = Number of years
Given:
Principal (P) = $300.00
Rate (R) = 2 1/4% = 2.25% = 0.0225 (in decimal)
Number of compounding periods per year (n) = 1 (as interest is compounded annually)
Time (T) = 3 years
Final amount on Account II = P * (1 + (R / n))^(n * t)
= $300.00 * (1 + (0.0225 / 1))^(1 * 3)
= $300.00 * (1 + 0.0225)^3
= $300.00 * (1.0225)^3
= $300.00 * 1.06684214
= $320.05 (rounded to the nearest cent)
So, Account II will have a final amount of $320.05 after 3 years.
Finally, we can calculate the total amount of money Emma will have at the end of 3 years by adding the principal amounts and the interest earned:
Total amount = Account I + Account II
= $500.00 + $320.05
= $820.05
Therefore, Emma will have a total of $820.05 at the end of 3 years if she makes no other deposits or withdrawals.