Business math word problem**********

Question

A loan of $50,000 at 7% is due in 16 months. Find the present value of the loan if the time value of money is 10%. 

Answer 1

The amount due in 16 months and considering annual compounding (the text of the problem does not say otherwise).. is equal to

50,000 x (1+7%)^(1.25) = 54,412.63.

Note: 16 months = 16/12 = 1.25 years.

If we pay it back today, the person who is owed the money can deposit the money he/she receives in a bank account and earn 10% interest annually. Hence the amount to return today would be

54,412.63 x 1/(1 + 10%)^(1.25) = 48,301.31.

The problem is about the application of the formulae for PV (present value) and FV (forward value).