IGCSE Economics 0455: How the Rate of Interest Affects Saving and Borrowing

Yusuf has $3000 in a savings account, earning his country's official rate of interest, currently 3% per year. He is also considering taking out a $4000 loan to renovate his kitchen, at the same 3% annual rate of interest. To keep the numbers simple, assume the same rate of interest applies to both his savings and this loan. The central bank has just raised the official rate of interest from 3% to 6%.

(a) Calculate the interest Yusuf's $3000 in savings would earn in one year, both at the original 3% rate and at the new 6% rate. [2]

(b) Calculate the extra amount Yusuf would need to repay in interest in the first year on a $4000 loan, both at the original 3% rate and at the new 6% rate. [2]

(c) Using your answers to (a) and (b), explain why a rise in the rate of interest from 3% to 6% is likely to make Yusuf more inclined to save and less inclined to borrow. [3]

Part (a): Interest earned on Yusuf’s savings

At the original rate of 3%, Yusuf’s $3000 in savings earns: $3000 \times 0.03 = 90$

This is $90 of interest in the first year.

At the new rate of 6%, the same $3000 earns: $3000 \times 0.06 = 180$

This is $180 of interest in the first year, exactly double the amount at 3%.

Part (b): Extra interest owed on the loan

At the original rate of 3%, the extra interest Yusuf would owe in the first year on a $4000 loan is: $4000 \times 0.03 = 120$

This is $120 of interest owed in the first year.

At the new rate of 6%, the extra interest owed on the same $4000 loan is: $4000 \times 0.06 = 240$

This is $240 of interest owed in the first year, again double the amount at 3%.

Part (c): Why the rise in the rate of interest changes Yusuf’s incentives

The rise in the rate of interest from 3% to 6% works on Yusuf’s saving and borrowing decisions in the same direction at once. On the saving side, his $3000 now earns $180 a year instead of $90, so simply leaving money in his savings account rewards him with twice as much extra income as before, making saving more attractive relative to spending it now.

On the borrowing side, taking out the $4000 loan would now cost him $240 in interest in the first year instead of $120, so the loan has become noticeably more expensive to repay. A more expensive loan is less attractive to take on, especially for a renovation that Yusuf could delay.

Because both effects point the same way (a bigger reward for keeping money saved, and a bigger cost for borrowing it) Yusuf has a stronger overall incentive to keep his $3000 saved and to hold off on the kitchen renovation loan than he did before the rate of interest rose.

Final answers

(a) $90 of interest at 3%; $180 of interest at 6%.
(b) $120 of interest owed at 3%; $240 of interest owed at 6%.
(c) The rise in the rate of interest both doubles Yusuf’s reward for saving and doubles the cost of borrowing, so he becomes more inclined to save and less inclined to take out the loan.