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# Get Rich Bank offers a mortgage bond at 13.5% p.a. over 10 years and Capital Bank...

bubbletrea | Student, Grade 11 | Honors

Posted September 11, 2013 at 3:32 PM via web

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Get Rich Bank offers a mortgage bond at 13.5% p.a. over 10 years and Capital Bank offers a mortgage bond at 10.5% p.a. over 25 years. Compare the repayments and the total amounts payable.

a) find the amount of repayment to each bank on a loan of \$80000

b) find which total amount paind will be less

durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted September 11, 2013 at 4:16 PM (Answer #1)

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To establish the repayment amount use the present-value formula: `P=(x[1-(1+i)^-n])/i`

Option 1: where P=\$80 000, i=13.5% (ie0.135) (compounded monthly) and n= 10yrs x 12 months

`80000=(x[1-(1+((13.5%)/12)^-(10 times12)]))/((13.5%)/12)`

`therefore 80000 times 0.01125= x[1-(1+0.01125)^-120]`

`therefore x=900/0.738798`

`= \$1218.19` (Option 1)

Option 2 : where P=80 000 i=10.5% (0.105) (compounded monthly) and n=25 yrs x 12 mnths

`therefore 80000=(x[1-(1+0.105/12)^-300])/(0.105/12)`

`therefore 80000 times 0.00875=x[1-(1.00875)^-300]`

`therefore x=700/0.926728399`

`therefore x=\$755.35` (Option 2)

Ans:

So we can see that option 2 is cheaper compared to option 1 on a monthly basis BUT

The total repayments however reveal that

Option 1 costs \$1218.19 x 120 = \$146 182.80

Option 2 costs \$755.35 x 300 = \$226 605.00

making Option 1 a much cheaper choice.

Sources:

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