A very weird loan, indeed!
Negative interest loans do exist. Generally, they occur when governments want to inject money into a stagnate economy.
This loan is weird even by those standards!
The loan is for one million (1 000 000) monetary units (what kind is up to you). That is not so strange.
The loan is made at the beginning of the day (you are welcome to pick what means). The loan is for 365 days with a payment due at the beginning of the day starting with the day after the loan. This is a little strange; but, not all that strange.
Now for the strange interest rate: -100% nominally of the entire period of the 365-day loan! Because you have to start making payments before the end of the loan before everything is discounted, you will have to pay some amount back, which turns out to be, very roughly, 60% of the loan.
The problem's question is: what is the uniform payment amount in your selected monetary units? It turns out to be very close to an integer. Round your answer to that integer and enter that integer as your answer.
The answer is 1591.
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1 solution
Effectively, what the lender is doing is buying an annuity from you for the present time payment of the loan amount. We have two problems to solve: what is the effective interest rate and what is the payment amount knowing the daily effective interest rate.
effectiveInterestRate = ( compoundingTimes nominalInterestRate + 1 ) compoundingTimes − 1 = ( 3 6 5 − 1 . + 1 ) 3 6 5 − 1 ≈ − 0 . 6 3 2 6 2 5 .
What we want do is solve for the payment amount:
( effectiveInterestRate + 1 ) ( 3 6 5 effectiveInterestRate + 1 − 1 ) effectiveInterestRate × payment = 1 0 0 0 0 0 0 ≈ 6 2 8 . 5 3 5 × payment = 1 0 0 0 0 0 0 → payment ≈ 1 5 9 1