I want a mortgage on a house worth £250000, for which I need to put up a deposit of 20%. I want a mortgage of 15 years, with an interest rate of 6%, paid monthly in arrears.

What is the monthly amount?

Mortgage amount: 80% of £250k = £200k

i = 0.06/12 = 0.005

n = 15*12 = 180

Solution:

The deposit required is 20%. So the mortgage amount will be 80% of 250,000 = 200,000 = M

The number of time periods is n = 15 * 12 = 180

(because the payments are monthly)

The interest rate is 6%/12 = 0.5% = 0.005 = i

We use this formula for the total amount of the mortgage 200,000

• (M / i) * [ 1 – {1/ (1 + i)}n]

So we have

200, 000 = Mi∗[1−{ 1

(1+i )n }]where M is the monthly payment

200,000 =M0.005

∗[1−{ 1(1+0.005 )180 }]

200,000 = M * 118.5

So M = 1687.71