# A person borrows \$10000 and agrees to repay a loan in equal instalments over 20 years. Interest is 12% pa on any money owing compounded quarterly. Solve this using the present value formula ( he needs the money now )

`P= (x(1- (1+i)^-n))/ i`   substitute all the known values

`10 000= (x(1-(1+ 0.12/4)^-(20times 4)))/ (0.12/4)`  The interest is divided by 4 because it is compounded quarterly. If it was compounded monthly it would be over 12...

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Solve this using the present value formula ( he needs the money now )

`P= (x(1- (1+i)^-n))/ i`   substitute all the known values

`10 000= (x(1-(1+ 0.12/4)^-(20times 4)))/ (0.12/4)`  The interest is divided by 4 because it is compounded quarterly. If it was compounded monthly it would be over 12 and so on. The 20 (years) - the exponent-  is multiplied by 4 to show that the years are compounded. Whatever you divide the interest by inside the bracket is the same as you will multiply the years (the exponent)

Take care to complete the steps in the correct order.

`10 000times 0.12/4` = `x( 1- (1.03)^-80)`

`300= x(1- 0.093977096` )

`300/ 0.906022904 = x`

x= \$331,12

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