Question

Suppose that you take out a 30-year mortgage loan of $200,000 at an interest rate of 10%.

1. What is your total monthly payment?

2. How much of the first month’s payment goes to reduce the size of the loan?

3. If you can afford to pay $2,000 per month, how long would it take you to pay

   for this loan (still at 10% interest)?

4. If you can only pay $1,700 per month, and still want to finish paying in 30

5. years, what is the highest (annual) interest rate that you could pay?

Answer 1

1)

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

200000= Cash Flow*((1-(1+ 10/1200)^(-30*12))/(10/1200))

Cash Flow = 1755.14

	Monthly rate(M)=	yearly rate/12=	0.83%
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid
1	200000.00	1755.14	1666.67	88.48

Where

Interest paid = Beginning balance * Monthly interest rate

Principal = Monthly payment – interest paid

2)

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

200000= 2000*((1-(1+ 10/1200)^(-n*12))/(10/1200))

n(in years) = 17.99

3)

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

200000= 1700*((1-(1+ Interest rate/1200)^(-30*12))/(Interest rate/1200))

Interest rate% = 9.63