Math  /  Numbers & Operations

QuestionIf you borrow $900\$ 900 for 4 years at an innual interest rate of 5%5 \%, how much will you pay altogether? \$[?]

Studdy Solution

STEP 1

1. The borrowed amount is $900\$ 900.
2. The duration of the loan is 4 years.
3. The annual interest rate is 5%5 \%.
4. The interest is compounded annually.

STEP 2

1. Use the formula for compound interest to calculate the total amount after 4 years.
2. Subtract the principal to find the total interest paid.
3. Add the principal and the total interest to find the total amount paid altogether.

STEP 3

Use the compound interest formula A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt} to calculate the total amount after 4 years, where: - PP is the principal amount (900900). - rr is the annual interest rate (0.050.05). - nn is the number of times interest is compounded per year (1, since it's annually). - tt is the time the money is invested for (4 years).
A=900(1+0.051)1×4 A = 900 \left(1 + \frac{0.05}{1}\right)^{1 \times 4}

STEP 4

Simplify the expression inside the parentheses.
A=900(1+0.05)4 A = 900 \left(1 + 0.05\right)^4 A=900(1.05)4 A = 900 \left(1.05\right)^4

STEP 5

Calculate 1.0541.05^4.
1.0541.21550625 1.05^4 \approx 1.21550625

STEP 6

Multiply the result by 900900 to find the total amount AA.
A=900×1.21550625 A = 900 \times 1.21550625 A1093.96 A \approx 1093.96

STEP 7

Subtract the principal amount from the total amount to find the total interest paid.
Total Interest=1093.96900 \text{Total Interest} = 1093.96 - 900 Total Interest193.96 \text{Total Interest} \approx 193.96

STEP 8

Add the principal amount to the total interest to find the total amount paid altogether.
Total Amount Paid=900+193.96 \text{Total Amount Paid} = 900 + 193.96 Total Amount Paid1093.96 \text{Total Amount Paid} \approx 1093.96
Solution: The total amount you will pay altogether is approximately $1093.96\$ 1093.96.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord