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What equal installment of annual payment will discharge a debt which is due as Rs. 848 at the end of 4 years at 4% per annum simple interest?

The above question can be calculated by using the formula $$x= \frac{100P}{100n+\frac{n(n−1)r}{2}}$$ which gives the result $= 200$. My doubt is that $200 \cdot 4 = 800$. So when will the balance $848-800= 48$ be paid?

N. F. Taussig
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kodewhiz
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2 Answers2

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*you are forgetting the interest on the payments *

Assuming payments at the end of each year,

interest of 4% for 3 years will accrue for 1st 200 when payment is due,

for 2 years for 2nd payment , etc.

The formula you used was devised taking this into account.

You can check that exactly 48 interest would have accrued at time of payment, you have paid the dues fully !

true blue anil
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  • Could you please elaborate. When we repay a loan, the installment amount already includes the interest. – kodewhiz Aug 27 '15 at 15:18
  • That would be so if the loan due was at the start, here the loan due is given at the end of 4 years, what you pay in instalments gathers interest till the time of payment. – true blue anil Aug 27 '15 at 15:25
  • So what exactly are we paying at the time of payment? 800 – kodewhiz Aug 27 '15 at 15:30
  • No, including accumulated interest, 848 – true blue anil Aug 27 '15 at 15:35
  • Still don't get it. – kodewhiz Aug 27 '15 at 18:10
  • Any loan - payment balance has to be computed at one point in time. Here we are computing at the end of 4 years. 1st payment of 200 becomes 200+12% interest = 224 at payment time 2nd payment of 200 becomes 200 + 8% interest = 216 at payment time 3rd payment of 200 becomes 200 + 4%interest = 208at payment time 4th payment of 200 remains 200 at payment time 224+216+208+200=848 fully repays loan which was due only at payment time. I suggest you carefully read your book to get a grasp of fundamental concepts. – true blue anil Aug 28 '15 at 03:36
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I also had the same problemn.My peer told me that bank receive the first payment after 1 year, and THEY invest it at 4% interest. So they get 3 years of interest on that .The payment made at end of first year has 3 years to earn simple interest at 4% per year. So t will be 3 for that.

But why 3 years or why not 1 year.

Saumyojit Das
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