Question

Debts of $7000 due in one and a half year, and $11000 due in three years are to be settled by a single payment one year from now. What is the size of that single payment if interest is 7.5% compounded monthly?

Answer 1

To calculate the size of the single payment, we can use the formula for the future value of a series of payments. Substituting the values into the formula, we can calculate the size of the single payment.

Step-by-step explanation:

To calculate the size of the single payment, we can use the formula for the future value of a series of payments, which is:

FV = P×[(1 + r)^n - 1]/r

In this formula, FV represents the future value, P is the amount of each payment, r is the interest rate per period, and n is the number of periods. In this case, the future value (FV) is the sum of the two debts, $7000 and $11000. The interest rate (r) is 7.5% divided by 12 to get the monthly rate. The number of periods (n) is the duration until the single payment, which is one year minus the time until each debt is due.

Substituting these values into the formula, we can calculate the size of the single payment.