What was the principal amount on a 20-year loan if the total amount paid was $5,800 and the interest rate was 6.6% compounded monthly?
The principal amount on a 20-year loan of $5,800 with a 6.6% interest rate compounded monthly is approximately $2,072.
Calculating the Principal Amount
Explanation: To determine the principal amount, we can use the formula for compound interest: FV = P (1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the interest rate, n is the number of times that interest is compounded per time period, and t is the time in years.
Given:
- FV (future value) = $5,800
- r (interest rate) = 6.6% or 0.066 as a decimal
- n (number of times interest is compounded) = 12 (monthly)
- t (time period) = 20 years
To find the principal amount, rearrange the formula to solve for P:
P = FV / (1 + r/n)^(nt)
By substituting the values into the formula:
P = $5,800 / (1 + 0.066/12)^(12*20)
P = $2,072
Therefore, the principal amount on a 20-year loan of $5,800 with a 6.6% interest rate compounded monthly is approximately $2,072.