A loan of SEK 27,000 is to be repaid in 3 equal amounts over 3 years.

Question

A loan of SEK 27,000 is to be repaid in 3 equal amounts over 3 years. The interest rate is 4.2%.

a) What is the total amount to be paid to the bank after one year?

b) How many percent more expensive will the loan be with interest? (Compared to an interest-free loan)

Answer 1

Well suppose the amount paid back is x

At the end of the first year

27000 + 0.042 x 27000 = 28134 is owed

x is paid

remaining debt = 28134 - x

At the end of the second year

owed 1.042 (28134-x)

paid x

remaining debt = 1.042 (28134-x) - x = 29315 - 2.042x

At the end of the third year

owed 1.042 (29315 - 2,042x)

paid x

remaining debt 1.042 (29315 - 2.042x) - x = 0

30546 - 3.13x = 0

x = 9759.18

Total paid back = 3 x = 29277.54

Interest free loan = 27000

Difference = 2277.54

% more expensive = (2277.54/27000) x 100 = 8.4 %