F4 - Repayments And The Cost Of Credit

Question 1

What is a mortgage?

Answer 1

A mortgage is a loan taken out to buy a property

Question 2

What is a student loan?

Answer 2

Used to help pay for further and higher education courses.

Question 3

What does APR stand for?

Answer 3

Annual Percentage Rate

Question 4

What is the APR?

Answer 4

The annual interest rate on loans

Question 5

What is the formula for APR?

Answer 5

m Ak
C = Σ ( ——– )
k=1 [1+i]^tk

C = amount of loan
m = number of payments 
i = APR (decimal)
Ak =amount of the 'k'th repayment 
tk = interval in years between the start of the loan and the 'k'th repayment

Question 6

You borrow £400 from a money lender to be paid back in 5 equal monthly instalments at an APR of 1509%
How much is the monthly payment, A?

Answer 6

C = 400, m = 5, i = 15.09, 
A = A1 = A2 = A3 = A4 = A5
tk = a fraction with the denominator 12 (12 months in a year)

So,
400 = A/(16.09)^1/12 + A/(16.09)^2/12…->…A/(16.09)^5/12
400 = A(0.793329+0.629371+0.499299+0.396108+0.314244)
400 = A x 2.63235
A = 151.9554
Monthly payments of £152