Question

Find the equated date at which the original payments are equivalent to the single payment. State your answer in years and months (from 0 to 11 months).

Original Payments
Interest Rate
Frequency

Answer 1

The monthly payments for a $300,000 30-year loan at 6% interest can be calculated using the present value of an annuity formula. Making the equivalent of 13 monthly payments a year accelerates the loan payoff and reduces the total interest paid.

Step-by-step explanation:

The calculation of a loan's monthly payment with a given interest rate and term length is an application of the time value of money concept in finance. For a $300,000 loan at a 6% annual interest rate, compounded monthly, over 30 years, the monthly payment can be calculated using the formula for the present value of an annuity. With these inputs, we will apply the formula:

PV = R (1 - (1 + i)^(-n)) / i,

where PV is the present value (loan amount), R is the monthly payment, i is the monthly interest rate, and n is the total number of payments.

By making 13 payments a year instead of just 12 (which effectively is a monthly payment increased by a fraction of 12), you effectively pay off the loan faster and save on the total amount of interest paid.