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

To find the present value (PV) of the loan, we can use the formula for present value in relation to the time value of money:

PV=FV(1+r)nPV=(1+r)nFV​

Where:

1. FVFV is the future value of the loan, which is $50,000.
2. rr is the time value of money, expressed as a decimal (10% = 0.10).
3. nn is the number of periods until the loan is due, expressed in years. Since the loan is due in 16 months, we convert this to years: n=1612=43≈1.33n=1216​=34​≈1.33 years.

Now, substituting the values into the formula:

1Calculate (1+r)n(1+r)n:

(1+0.10)1.33≈1.101.33≈1.133(1+0.10)1.33≈1.101.33≈1.133

2Calculate the present value:

PV=500001.133≈44167.67PV=1.13350000​≈44167.67

Thus, the present value of the loan is approximately $44,167.67.