Adam and Eve need to borrow $115,000 to purchase a cave and are debating whether

Question

Adam and Eve need to borrow $115,000 to purchase a cave and are debating whether they should use a 20-year mortgage or 30-year mortgage. They also want to know the effect of two interest rates, a 6% and 8%, on:

MONTHLY PAYMENT

Term of the Mortgage

Interest rate 6%

Interest Rate 8%

20 years

30 years

TOTAL COST

Term of the Mortgage

Interest rate 6%

Interest Rate 8%

20 years

30 years

TOTAL INTEREST PAID

Term of the Mortgage

Interest rate 6%

Interest Rate 8%

20 years

30 years

Term of the Mortgage

Interest rate 6%

Interest Rate 8%

20 years

30 years

Explanation / Answer

Monthly payment = A/D

(D) = {[(1 + i) ^n] - 1} / [i(1 + i)^n]

A = 115,000

MOnthly payment for 6%

n = 240 (20 years times 12 monthly payments)

i = 0.005 (6% annually expressed as .06, divided by 12 monthly payments per year)

D = =(((1+0.005)^240)-1)/(0.005*(1+0.005)^240)

D = 139.58

MOthly PAyment = 115,000 / 139.58 = 823.90

Now, for 30 years,

n = 360 (30 years times 12 monthly payments)

i = 0.005 (6% annually expressed as .06, divided by 12 monthly payments per year)

D = =(((1+0.005)^360)-1)/(0.005*(1+0.005)^360)

D = 139.58

MOthly PAyment = 115,000 / 166.79 = 689.48

Now, for 8%

n = 240 (20 years times 12 monthly payments)

i = 0.00667 (8% annually expressed as .08, divided by 12 monthly payments per year)

D = =(((1+0.00667)^240)-1)/(0.00667(1+0.00667)^240)

D = 119.581

MOthly PAyment = 115,000 / 119.581 = 961.69

NOw, for 30 years

n = 30 (30 years times 12 monthly payments)

i = 0.007 (8% annually expressed as .08, divided by 12 monthly payments per year)

D = =(((1+0.00667)^360)-1)/(0.00667*(1+0.00667)^360)

D = 136.23

MOthly PAyment = 115,000 / 136.23 = 844.16

Total Cost

Total Loan Cost = =+(r*A*n)/(1-(1+r)^(-n))

A = 115,000, r = 0.005 & 0.00667, n = 240 and 360

For 6% and 20 years

Total Loan Cost = (0.005*115000*240)/(1-(1+0.005)^(-240))

                          =   197734.97

Similarly for all,

Total Interest paid

Total Interest paid = Total Loan cost - A (The borrowed amount)

For 6%, 20 years loan

Total Interest paid = =197,734.97 - 115,000 = 82,734.97

Similarly for all,

Monthly Payment Term of Mortagage 6% 8% 20 years 824 962 30 years 689 844

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