Is there an equation for calculating future value of constant payments at variable interest rate

lordy888

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Jan 6, 2021
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My task is to calculate the future value of constant payments at variable interest rate as follows:

Say the principal is 10,000. Annual rate is 5%. Tenor with 2 monthly period starting at Jan. The periodic payment in arrear is 1,300.

Interest for Jan is calculated as (10,000 * 5% * 31 / 360 = 43) The principal repaid is (1,300 - 43) = 1,257.

Interest for Feb is calculated as ((10,000-1,257) * 5% * 28 / 360 = 34) The principal repaid is (1,300 - 34) = 1,266.

The future value (aka balloon payment) would be 10,000 - 1,257 - 1,266 = 7,477.

So I would like to know if there is a calculation could be used to result 7,477 by inputting the above data, rather than calculate the whole repayment schedule every each time.

I tried excel formula to see if it solved the situation, and the excel formula failed:
  1. FV function: future value of constant payments at constant interest rate
  2. FVschedule function: future value of no payments at variable compound interest
Thank you for your help.
 

JeffM

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Sep 14, 2012
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I doubt that there is such a formula.

What do you mean by “tenor”. Maturity?

You do not have a variable interest rate. You have a variable length of period.

Can you give the exact wording from your text book?
 

lordy888

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Jan 6, 2021
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Hi Sir Jeffm.
Tenor meant the repayment period or maturity. In the above case, it means the loan is repayable in full within 2 months.
Thank you.
 

JeffM

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The question does not make much sense. You say constant payment, but there seem to be only two payments, and they are not equal. And what is with the implied 360-day year?

Please quote the problem exactly as it is given in your text.
 

lordy888

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Please note that the constant payment is 1,300 for each period and a balloon payment of 7,477 at the end of the period. Total payments are (1,300*2 + 7,477) =10,077, comprised of 10,000 principal and (43+34) = 77 interest.
360 day per year is so called Actual/360 day count convention. It is broadly used by loan shark in order to increase the implicit interest rate.
You may refer to https://en.wikipedia.org/wiki/Day_count_convention for further information.
Please let me know if you need further information to help with the question. Thank you Sir JeffM.
 

JeffM

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There is no formula.
 

lordy888

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Jan 6, 2021
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Thank you.
 
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