Question

You have a loan outstanding it requires making five annual payments of $3.000 each at the end of the next five years Your bank has offered to allow you to skp making the next four payments in lieu of making one large payment at the end of the taste in five years in the interest rate on the oan is 1%, what final payment will the bank require you to make so that it is indiferent to the two forms of payment?

Answer 1

Step-by-step explanation:

The final payment that the bank will require you to make so that it is indifferent to the two forms of payment is $12,000.

Here’s how to calculate it:

The present value of the five payments is:

PV = 3000/(1+0.01)^1 + 3000/(1+0.01)^2 + 3000/(1+0.01)^3 + 3000/(1+0.01)^4 + 3000/(1+0.01)^5

PV = $13,828.16

Copy

If you skip the next four payments and make one large payment at the end of the fifth year, then the present value of that payment is:

PV = X/(1+0.01)^5

Copy

where X is the amount of the final payment.

Since the bank wants to be indifferent between these two forms of payment, we can set these two present values equal to each other and solve for X:

13,828.16 = X/(1+0.01)^5

X = $12,000

Copy

Therefore, the bank will require you to make a final payment of $12,000 so that it is indifferent to the two forms of payment.