SOLUTION: How much does a money lender earns in a year when he starts with 9900 dollars capital if he loans it at 900 dollars per person payable in 5 months at 200 dollars per month. Assumin

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Question 1122275: How much does a money lender earns in a year when he starts with 9900 dollars capital if he loans it at 900 dollars per person payable in 5 months at 200 dollars per month. Assuming that he further loans his monthly collection at the same rate, how much will he earn in one year? Thanks.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
he starts the year with 9900 capital.

he loans the full amount to 11 persons (11 * 900 = 9900)

each of those 11 persons pays him 200 dollars at the end of each month for 5 month.

11 * 200 = 2200 total payments at the end of each month for 5 months

the interest rate per month will be 3.618024838%.

multiply that by 12 and the nominal interest rate per year is 43.41629805%.

his total interest earned will be the future value of those payments minus the original investment = 11,825.28843 - 9,900 = 1,925.288426.

this can be seen in the following excel spreadsheet printout.

$$$

i used the TI-BA-II financial calculator to find the interest rate and the future value of the payments.

i also used excel to do the same thing.

there is an online calculator that you can use that will provide you with similar results.

those results, however, will be rounded somewhat, although not enough to change anything significantly.

that calculator can be found at https://arachnoid.com/finance/

the inputs to the calculator were:

present value = -9900 (negative because it's money going out)
future value = 0
number of time periods = 5 (investment is for 5 months)
payment amount = 2200 each month (positive because it's money coming in).
payment is made at the end of each month.

you click on IR and the calculator tells you that the interest rate each month is 3.618025%.

that's the same as 3.618024838% rounded to 6 decimal digits.

here's a display of those inputs and output.

$$$
to find the future value of the investment, your inputs are:

present value = 0
future value = 0
number of time periods = 5 (investment is for 5 months)
payment amount = -2200 each month (negative because it's assumed to be money going out, i.e. you are investing 2200 each month into your own account - kind of quirky, but that's the way the calculator works. if you want your future value to be positive, the monthly payments have to be negative).
interest rate per time period = 3.618025%
payment is made at the end of each month.

you click on FV and the calculator tells you that the future value is 11,825.29

here's a display of those inputs and outputs.

$$$