Question

These questions do not have data. These are conceptual, it is just asking on a basis of how would you do this in most generic forms of these questions.

A) How would you solve for the “PMT” in an annuity and perpetuity problem?

B) How would you determine which of the 3 “PMTs” you need to solve for?

C) What would the time subscripts in the PVA and PVP formulas tell us?

D) How would you solve for targeted savings by retirement and savings required to reach that target?

Answer 1

A) The PMT is the equal Periodic payments done during an annuity or perpetuity. On paper, we can solve PMT using the formula.

For Annuity; PV = PMT (1-1/(1+r)ⁿ) / r & For Perpetuity, PV = PMT/r

However, its very easy to solve on Excel sheet using the following formula:

PMT( interest_rate, number_payments, PV, [FV], [Type] )

B) The three PMT's are PMT, IPMT & PPMT

PMT: If the cash flows form annuity or perpetuity, we solve for PMT

IPMT: If the interest payment (IPMT) at a particular period for an investment or Loan based on an interest rate and a constant payment schedule is asked, we solve for IPMT

Excel formula for IPMT is IPMT( interest_rate, period, number_payments, PV, [FV], [Type] ) where period indicates the n^th period at which the interest payment IPMT is calculated

PPMT: If the Principal payment (PPMT) at a particular period for an investment or Loan based on an interest rate and a constant payment schedule is asked, we solve for PPMT

Excel formula for PPMT is PPMT( interest_rate, period, number_payments, PV, [FV], [Type] ) where period indicates the n^th period at which the principal payment IPMT is calculated

C) The time subscript in the PVA (Present Value of Annuity) & PVP (Present Value of Perpetuity) formulae tell us the time period to which all the cash flows of the annuity & perpetuity are discounted.

D) Targeted Savings for retirement is nothing but the present value of all those future withdrawals a person wish to make after the retirement. We just build a timeline consisting of all his future withdrawals after retirement and discount all of them to find their present value which is the targeted savings needed.

Savings required to reach that target are the contributions made by the person from the time he decided to save to till the date he decided to make contributions to the retirement fund so that, the present value of all these savings equals to the targeted savings calculated by us above.