Question

A debt of $5000 due in three months and another of $2000 due in five months are to be settled by a single payment at the end of nine months. Find the size of this payment using the present as the focal date. Assuming money is worth 5% per annum simple interest.

Answer 1

To find the size of the payment at the end of nine months for two debts, calculate the present values of each debt using the present value formula and the given interest rate. Add the present values of the two debts to find the size of the payment.

Step-by-step explanation:

To find the size of the payment at the end of nine months, we need to calculate the present value of the two debts. The formula to calculate the present value (PV) of a future value (FV) is:

`PV = FV / (1 + r)^n`

Where r is the interest rate and n is the number of periods. Firstly, let's calculate the present value of the $5000 debt due in three months:

`PV1 = $5000 / (1 + 0.05)^3 = $5000 / 1.05^3 = $5000 / 1.157625 = $4322.36`

Next, calculate the present value of the $2000 debt due in five months:

`PV2 = $2000 / (1 + 0.05)^5 = $2000 / 1.05^5 = $2000 / 1.276281 = $1568.53`

Finally, add the present values of the two debts to find the size of the payment at the end of nine months:

Size of payment =
`PV1 + PV2 = $4322.36 + $1568.53 = $5882.89`