Abank agrees to lend via simple loan $100 today to thomas. the agreement is based on that the yearly interest rate is 15%. if thomas must pay back the loan in 10 years, how much will he be required to reimburse to the bank?

$404,55 (cumulative) or $250 (american)

Explanation:

This explanation considers a cumulative interest rate in the simplest way. And american amortization system. Consider that there is also French and German systems which works differently depending on the way the loan reimbursed

Cummulative Interest Rate:

Consider this:

If Thomas had to return it in one year he would have to return $115 ($100+15%) which is equal to 100*(1+0.15)

Now, at the begining of the second year, his debt is $115, and at the end its $115+15% = 132,25.  Which is equal 100*(1+0.15)*(1+0.15), this is equivalent to 100*(1+0.15)^{2}

The general formula for cummulative interest is C(1+i)^{n}

Where

C = is the loan amount [in this case: 100]

i = is the interest rate [in this case: 0.15]

n = is the number of periods until [in this case: 10]

American System

The american system is quite straight forward:

Thomas should pay $15 every year for 10 years, and with the last payment he should pay $115.

This is because in this system Thomas returns the capital (the amount of the loan) at the end; and each year he only pays the interest .

$15*10 + $100 = $250