Suppose you borrow $220,000 to purchase a home. The loan will be repaid over the

Question

Suppose you borrow $220,000 to purchase a home. The loan will be repaid over the course of 30 years with equal monthly payments. The annual interest rate on the loan is 4.2% compounded monthly, giving monthly payments of $1,075.84.

A.) How much interest is due on the first payment? How much interest is due on the second payment?

B.) What will the unpaid loan balance be after 10 years of payments?

C.) If you can afford monthly payments of $1,400, then how much could you have borrowed under the same loan conditons (interest rate and number of payments)?

Explanation / Answer

Suppose you borrow $220,000 to purchase a home. The loan will be repaid over the course of 30 years with equal monthly payments. The annual interest rate on the loan is 4.2% compounded monthly, giving monthly payments of $1,075.84.

A.) How much interest is due on the first payment? How much interest is due on the second payment?

Interest is due on the first payment = 220000*4.2%/12 = $ 770

Balance available after first payment = 220000 - (1075.84 -770) = $ 219,694.16

Interest is due on the second payment = 219,694.16*4.2%/12 = $ 768.93

B.) What will the unpaid loan balance be after 10 years of payments?

unpaid loan balance be after 10 years of payments = fv(rate,nper,pmt,pv)

unpaid loan balance be after 10 years of payments = fv(4.2%/12,120,1075.84,-220000)

unpaid loan balance be after 10 years of payments = $ 174,486.99 or $ 174,487

C.) If you can afford monthly payments of $1,400, then how much could you have borrowed under the same loan conditons (interest rate and number of payments)?

Amount Can be borrowed = pv(rate,nper,pmt,fv)

Amount Can be borrowed = pv(4.2%/12,360,1400,0)

Amount Can be borrowed = $ 286,288.51 or $ 286,289

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