Question

For 1≤n≤10, find a formula for pn, the payment in year n on a loan of 100000 dollars. Interest is 3 percent per year, compounded annually, and payments are made at the end of each year for 10 years. Each payment is 10000 dollars plus the interest on the amount of money outstanding.

p(n)=

Answer 1

Answer: Pn= 10000(1+ 0.03(11-n))

Explanation:

From the question it is given that

Pn= 10000 + 3% 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= 100000

D2=100000-10000

Dn=100000-10000(n-1) eqn2

Therefore, substituting eqn2 into eqn1

Pn= 10000+3% of (100000-10000(n-1))

Pn= 10000+ 0.03(100000 - 10000(n-1))

Pn= 10000(1+ 0.03(10 - (n-1)))

Pn= 10000(1+ 0.03(11-n))