My relatives asked me this question and I didn't know how to answer. They wanted to compare which system is more profitable.
System 1:
The bank already holds their money for 3 years to give them a 15% interest rate minus 220 yearly fee. The amount held is 36,000. They are getting paid monthly. They get 450 a month excluding the fees.
Yearly income = 36,000 * 15% - 220 = 5180
3 year income = 5180 * 3 = 15,540
System 2:
In addition to the previous system, they want to take a 3-year loan to buy an asset like (a car, jewellery, stock market,...). The value of the asset will increase over the time. The fees of the loan are:
- 1.5% of the loan amount one time payment.
- 10 every 3 month.
Because of being paid monthly from the previous system, they want to pay 425 a month for the loan. Which means that they will pay a total of 15300 during the period of the loan. Now, they want to know what is the minimum loan amount that should be offered by the bank to make the second system better knowing that the asset may make them earn 10 - 12 % of it's value per year.
Solution :
Assuming the loan amount = x
If the interest rate of the loan is equal to the interest rate of the asset, this will be the critical point.
Interest rate of the loan for 3 years = $ \frac{15300 - (x - fees) }{x} $
fees = 0.015 x - 120
10% * 3 = $ \frac{15300 - (x - 0.015 x - 120) }{x} $
The minimum loan amount = 12000
Are my calculations correct?