Question

For 0 < or = n < or =10, find a formula for Pn, the payment in year n on a loan of 105000 dollars. Interest is 7 percent per year, compounded annually, and payments are made at the end of each year for 10 years.
Each payment is 10500 dollars plus the interest on the amount of money outstanding.
10500*1.07^n doesn't seem to be the right answer.

Answer 1

Answer: Pn= 10500(1+ 0.07(11-n))

Step-by-step explanation:

From the question it is given that

Pn= 10500 + 7% of Dn eqn 1

Where Pn is payment at year n

And Dn is outstanding debt at year n

n= 1,2,3...,10

D1= 105000

D2=105000-10500

Dn=105000-10500(n-1) eqn2

Therefore, substituting eqn2 into eqn1

Pn= 10500+7% of (105000-10500(n-1))

Pn= 10500+ 0.07(105000 - 10500(n-1))

Pn= 10500(1+ 0.07(10 - (n-1)))

Pn= 10500(1+ 0.07(11-n))