If my mother can repay me $300 in the first year $400 in the second year and $200 in the third year I would lend her the amount of $640 to feed me and my eight brothers and sisters at the rate of 12% compounded annually.
What is compound interest?
Compound interest is the interest which is calculated on the principle amount as well as on the interest amount that is being earned on the principle amount during the time it was being given as a loan.
The formula of compound interest is [tex]A= P (1+r)^t[/tex]
By adding the amount that can be recieved from the mother in three years that is [tex]\rm \$300 + \$400 + \$200 = \$900\\[/tex].
When we reverse the compounding of this amount at the rate of 12% for three years to obtain the present value of the amount, we get $640 as the amount that can be lended to the mother.
Formula:- [tex]P \times (\dfrac{1}{1+r})^n[/tex]
[tex]A= \$900 (\dfrac{1}{1.12})^3[/tex]
[tex]A= \$640[/tex]
Therefore, the amount that could be lended to mother at the rate of 12% is $640.
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