# math - loans

if i have to pay back a loan of 10 million over the next 5 yrs. How much are my yearly payments if each subsequent payment is 15% less than the previous year?

What is the interest rate? Zero?

If there is zero interest rate on the remaining balance, and if the first payment occurs at the end of the first year, then let the first payment be X and you have
X + 0.85 X + (0.85)^2 X + (0.85)^3 X = 10^6.
3.186625 X = 10^6
Solve that for X.
X = \$313,811.63
next payment = \$266,739.89
etc.

I made two careless errors in my previous answer. The total amount due is 10 million, not one million, and I forgot to ionclude the fifth payment.
The series of five payments ends with the one at the end of the fifth year, (0.85)^4*X
This makes a total payment of 3.70863125X equal to 10 million dollars. The first payment (X) should be X = 2,696,412

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