Calculating the principal

Question

By which formula shall I calculate the amount for the following problem:

Let say I want to buy a product, for which, I need to pay monthly installment of Rs500 , for 3 Months and rate of interest is 12% per annum.

The amount which needs to be deposited in saving bank account is ?.

Here its 1470.

Similarly for 6000 to be received in 3 months the rate of interest is 5.9 Amount deposited = 17824.

500 - Per month

2 - time in month

0 - Rate of interest p.a --> Principal =1000

Not able to understand the formula to calculate the amount deposited

Answer 1

The formula is

$PV=a\cdot \left( \Large{ \frac{(1+\frac{i}{12})^m-1}{\frac{i}{12}}}\right) \cdot \Large{\frac{1}{(1+\frac{i}{12})^m}}$

PV:= Present Value

a:= Annuity

i:= Annual percentage rate

m:= Number of months

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In your second example the calculation is

$PV=6000\cdot \left( \Large{ \frac{(1+\frac{0.059}{12})^3-1}{\frac{0.059}{12}}}\right) \cdot \Large{\frac{1}{(1+\frac{0.059}{12})^3}}\normalsize{\approx 17,824.44}$