Mary takes a loan of \$12000 to buy a car. This loan is consolidated with her current home loan at 7.9%p.a over a 15 years term, calculated monthly with monthly repayments. Calculate the increase...

Mary takes a loan of \$12000 to buy a car. This loan is consolidated with her current home loan at 7.9%p.a over a 15 years term, calculated monthly with monthly repayments.

Calculate the increase in home loan monthly repayments and the total interest charged over 15 years.

durbanville | Certified Educator

As we know how much Mary needs now, we can use the 'Present Value Formula' to calculate:

`P=(x[1-(1+i)^-n])/i`

where P=\$12 000 n=15 years x 12 (compounded monthly) and

i=7.9% which is `0.079/12`    also because of compound interest

`therefore 12 000 =(x[1-(1+(0.079/12))^-(15 times 12)])/(0.079/12)`

`therefore 12 000 times (0.079/12) = x[1-(1.306935881)^(-180)]`

`therefore (12 000 times 0.079/12)/(1-(1.306935881)^-180)=x` (Care not to round off too soon)

`therefore x=\$79.00`

If Mary is paying \$79 extra per month for 15 years (180 months) she will pay \$14 220 - \$12 000 in interest = \$2220

Ans: Mary's home loan will increase by \$79,00 per month and interest will amount to \$2220

durbanville | Certified Educator

Only saw your request today. My apologies for not replying sooner. Please post your question separately with attachments (they did not post on this one). The subject should be Science rather than Math. Thank you.