Math  /  Numbers & Operations

QuestionIf you borrow $700\$ 700 for 4 years at an annual interest rate of 8%8 \%, how much will you pay altogether?

Studdy Solution

STEP 1

1. The loan amount (principal) is $700.
2. The interest rate is an annual rate of 8%.
3. The loan duration is 4 years.
4. The interest is compounded annually.
5. We are using the formula for compound interest to find the total amount to be paid.

STEP 2

1. Define the formula for compound interest.
2. Substitute the given values into the formula.
3. Calculate the total amount to be paid.
4. Interpret the result as the total payment.

STEP 3

The formula for compound interest is:
A=P(1+rn)nt A = P \left(1 + \frac{r}{n}\right)^{nt}
where: - A A is the amount of money accumulated after n n years, including interest. - P P is the principal amount (the initial amount of money). - r r is the annual interest rate (decimal). - n n is the number of times that interest is compounded per year. - t t is the number of years the money is invested or borrowed for.

STEP 4

For our problem, we have: - P=700 P = 700 - r=0.08 r = 0.08 - n=1 n = 1 (since interest is compounded annually) - t=4 t = 4
Substitute these values into the compound interest formula:
A=700(1+0.081)1×4 A = 700 \left(1 + \frac{0.08}{1}\right)^{1 \times 4}

STEP 5

Simplify the expression inside the parentheses:
A=700(1+0.08)4 A = 700 \left(1 + 0.08\right)^4 A=700(1.08)4 A = 700 \left(1.08\right)^4

STEP 6

Calculate 1.084 1.08^4 :
1.0841.36049 1.08^4 \approx 1.36049

STEP 7

Multiply the principal amount by this result:
A=700×1.36049 A = 700 \times 1.36049 A952.343 A \approx 952.343

STEP 8

Therefore, the total amount to be paid after 4 years is approximately:
952.34 \boxed{952.34}

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