Answer to Question #128657 in Financial Math for Nyarinda

Question

SIMS lecturer has 3 options on repayment for a KES 25Mn - 20yr mortgage. He can make payments
monthly, quarterly or half yearly. For an effective annual rate of interest 9% calculate the total interest
that will be paid in each of the 3 options over the 20-year period.

Answer 1

I=A - {p (1+r/n) ^{n t}

Where;

P=25mn, R=9% or 0.09, T=20 and N=12 

Therefore;

A=25mn (1+9/1200)^20×12                  i.e.  9%=0.09 divided by the number of months per year

        0.09/12

   =25mn (1.0075)²⁴⁰

 = 150.22Mn

I=A-P

I=150.22-25

 125.22Mn monthly interest.

A=25(1+9/400)^20×4

 = 25(1+0.0225)⁸⁰

   ⁼25(1.0225)⁸⁰

  =148.25Mn

I=148.25-25

 =123.25Mn quarterly interest.

A=25(1+9/200)^20×2

 = 25(1+0.045)⁴⁰

 = 25(1.045)⁴⁰

  =145.40

I=145.40-25

=120.40Mn half yearly interest