a loan of 6000 over 5 years at 15 pa interest charged montlh

a loan of $6000 over 5 years at 15% p.a. interest, charged montlhy, is paid back in 5 yearly instalments. how much iseach instalment, and how much money is paid together?

Solution

Let each equal instalment be $x.

A= Amount of money for loan after 5 years

[A=6000(1+15/1200)^60]

[=6000(1.0125)^60]

[=12643.08]

[A_1=] Amount for first instalment after four year

[A_1=x(1.0125)^48]

Similarly we can calculate amount for second , third ,fourth and fifth

instalments.

[A_2=x(1.0125)^36]

[A_3=x(1.0125)^24]

[A_4=x(1.0125)^12]

[A_5=x]

Thus

[A_1+A_2+A_3+A_4+A_5]

[=x(1.0125^48+1.0125^36+1.0125^24+1.0125^12+1)]

[=x(1.0125^60-1)/(1.0125^12-1)]

[=6.8874x]

So

[12643.08=6.8874x]

[x=1835.68]

Thus each installment will be $1835.68 .

Total money paid together = 5 x 1835.68=$9178.40