Cullumber Company is considering an investment that will return a lump sum of $580,000 5 years from now. What amount should Cullumber pay for this investment in order to earn a 4% return?
The correct answer and explanation is:
To determine how much Cullumber Company should pay now to receive $580,000 five years from now and earn a 4% return, we use the concept of present value (PV). The formula for the present value of a lump sum is: PV=FV(1+r)nPV = \dfrac{FV}{(1 + r)^n}
Where:
- PVPV is the present value (what Cullumber should pay now)
- FVFV is the future value, which is $580,000
- rr is the annual interest rate, which is 4% or 0.04
- nn is the number of years, which is 5
PV=580,000(1+0.04)5=580,0001.2166529≈476,667.51PV = \dfrac{580{,}000}{(1 + 0.04)^5} = \dfrac{580{,}000}{1.2166529} \approx 476{,}667.51
Correct Answer: $476,667.51
Explanation:
The idea behind present value is that money available now is worth more than the same amount in the future because it can be invested to earn interest. In this problem, Cullumber wants to know how much it should invest today to get a future return of $580,000 in five years, assuming a desired rate of return of 4%.
The present value formula accounts for how interest compounds over time. In this case, the future amount of $580,000 is being discounted at an annual rate of 4% over 5 years. Each year, the value of money decreases when projected backward, which is why we divide rather than multiply. This gives the amount that should be paid today so that when it grows at 4% annually, it becomes $580,000 at the end of 5 years.
If Cullumber pays exactly $476,667.51 now, and the investment grows at a 4% annual rate, it will reach the target of $580,000 in 5 years, fulfilling the company’s return requirement.