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What annual payment will discharge a debt of $\$770$ due in 5 years, the rate of interest being $5\%$ per annum? What I am doing is $(5\% \text{ of } \$770 ) + (\$770 / 5) = \text{ annual payment}$. The book which I am referring to gives $\$140$ as the answer. How would that be?

md2perpe
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Jigar Trivedi
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    I think the problem is worded poorly. The $770$ is the forward value of the debt? If so then you are looking for $P$ such that $\sum_{i=0}^4 P\times (1+.05)^i=770$ which yields $P=\frac {770}{\sum_{i=0}^4 (1+.05)^i}=139.351$ which I guess you could round to $140$. – lulu Jul 17 '17 at 17:34
  • At 5% interest per annum, the present value of 5 annual payments of $$140$ beginning in one year is $$606$, so @lulu must have the correct interpretation. – John Wayland Bales Jul 17 '17 at 18:10
  • Thank you guys for commenting. @lulu, I did not get how you ended up here. Could you please explain in simplest words? I am beginner in mathematics. What I interpreted is this: 770 is lent. On that 5% interest is there per annum. So, per year one has to pay 154 (770/5) + 38.5 (5% of 770) = $192.5 – Jigar Trivedi Jul 18 '17 at 16:33
  • Ok. Because you told me that the official answer was $140$ I looked for an interpretation that gave me that answer, or at least close to it. Best I could come up with was: The debt I owe is $770$ payable in $5$ years. That means, to discharge the debt I just have to pay exactly $770$ five years from today. To discharge the debt I intend to pay $P$ every year from now till then. Note that the $P$ I pay in year $5$ will be worth exactly $P$ in year $5$ (obviously). The $P$ I pay in year $4$ will be worth $1.05P$ in year $5$ and so on. Hence my formula, which yields $P=139.351$. – lulu Jul 18 '17 at 16:37
  • If you want to get to $$140$ exactly, use simple interest: the first $$140$ paid at the end of the first year accrues $5%$ i.e. $$7$ a year for the remaining $4$ years, and similarly the other payments of $$140$ so after five years you end up with $$140 \times 5 +$7 \times (4+3+2+1+0) = $770$ with which to pay off the debt. The real world does not work like this – Henry May 16 '18 at 07:18

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