Question

A demand loan of ​$6000.00 is repaid by payments of ​$2500.00 after two ​years, ​$2500.00 after four​years, and a final payment after seven years. Interest is 9​% compounded quarterly for the first two years, 10​% compounded semi-annually or the next two ​years, and 10​% compounded annually thereafter. What is the size of the final payment?

Answer 1

The size of the final payment on the demand loan is $6793.41.

Step-by-step explanation:

To find the size of the final payment on the demand loan, we need to calculate the remaining balance after all the previous payments have been made.

After two years, with 9% interest compounded quarterly, the remaining balance can be found using the formula:

P = A(1 + r/n)^(nt)

Where P is the remaining balance, A is the initial loan amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Using the formula with A = $6000.00, r = 0.09, n = 4, and t = 2, we get:

P = 6000(1 + 0.09/4)^(4*2)

P ≈ $6459.81

After four years, with 10% interest compounded semi-annually, the remaining balance can be found using the same formula:

P = 6459.81(1 + 0.10/2)^(2*2)

P ≈ $6555.10

Finally, after seven years, with 10% interest compounded annually, the remaining balance can be found using the formula:

P = 6555.10(1 + 0.10/1)^(1*(7-4))

P ≈ $6793.41

Therefore, the size of the final payment is $6793.41.