Loans question (1 Viewer)

[enigma_1]

A loan of $6000 over 5 years at 15% p.a interest, charged monthly, is paid back in 5 annual instalments.

a) What is the amount of each instalment?
b) How much is paid back altogether?

How do I work this out?

Answers:

(a) $1835.68 (b) $9178.41

 

[braintic]

(a)

Let Y be yearly instalment
A_0 = 6000
A_1 = 6000 (1.0125)^12 - Y
A_2 = A_1 (1.0125)^12 - Y = 6000(1.0125)^24 - Y(1+1.0125^12)
.
.
.
A_5 = A_4 (1.0125)^12 - Y = 6000(1.0125)^60 - Y(1+1.0125^12+1.0125^24+1.0125^36+1.0125^48) = 0

Y [(1.0125^12)^5 - 1] / [1.0125^12 - 1] = 6000(1.0125)^60

Y = 6000(1.0125)^60 (1.0125^12 - 1) / [(1.0125^60 - 1]

= $1835.68

(b) previous answer times 5