The amount of interest that accumulates on a $10,000 loan depends on several factors, including the interest rate and the repayment terms.
A simple interest loan charges interest only on the principal balance, that is, the amount of the original loan still outstanding. To calculate simple interest on a $10,000 loan, use the following formula:
Is = $10,000 r t
Where I is the accumulated interest, r is the annual interest rate and t is the length of the loan, expressed as a fraction of a year.
As an example, if your annual interest rate was 6 percent, multiply $10,000 by 0.06 to calculate the interest of $600 in a year. If the loan was only for three months, however, multiply that result by ¼ to calculate the quarter's simple interest of $150. If it were a 5-year loan, multiply $600 by 5 to get $3,000. In this case, the fraction was the whole number 5.
A compound interest loan charges interest on the principal balance and any interest already accumulated. To calculate the amount of compound interest on your loan, use the formula:
Ic = $10,000 (1 + (r / n))^(n t) - $10,000
Where n is the number of periods in a year. The other variables are the same as in the simple interest formula.
If the example's 5-year loan compounded monthly, divide the annual interest rate of 0.06 by 12 to calculate the monthly interest rate of 0.005. Add 1 to that number and raise the result to the total number of periods, calculated by multiplying 12 periods per year times 5 years, which is 60. Multiply the resulting 1.3489 times $10,000 to get the total due of $13,489. Finally, subtract the original $10,000 principal to calculate the interest of $3,489. As you can see, compound interest has the potential to significantly increase the amount of accumulated interest when compared to simple interest.
Annuities With Monthly Payments
Most lenders, such as those issuing car loans or mortgages, expect regular monthly payments that include interest and principal payments. These regular monthly payments function like an annuity. Because you're reducing the principal balance every month, the amount of interest that accumulates is likewise reduced. To determine the interest accumulated on a $10,000 loan, first calculate the monthly payments using the formula:
PMT = ($10,000 (r / 12)) / (1 - (1 + r / 12) ^ (-12 n))
By plugging in your data, you derive the monthly payment of $193.33. With that, you can calculate the total interest paid at the end of the loan using the formula:
Ia = PMT 12 t - $10,000
Thus, $193.33 times 60 payments equals $11,600. Subtracting the original loan amount leaves you with the interest of $1,600. Although an annuity employs compound interest, the total interest paid is less than even simple interest, because you're constantly reducing the principal.
The amount of interest you ultimately pay depends on the interest rate. Higher interest rates will add more interest to your payoff than lower interest rates. To get an idea how much interest rates affect your loan, consider these examples of the total interest you'll pay for each type of 5-year, $10,000 loan:
- A 1 percent interest rate accumulates $500 in simple interest, $512 in compound interest or $256 in annuity interest.
- A 10 percent interest rate accumulates $5,000 in simple interest, $6,453 in compound interest or $2,748 in annuity interest.
- A 30 percent interest rate accumulates $15,000 in simple interest, $33,998 in compound interest or $9,412 in annuity interest.