Investment X offers to pay you $6,000 per year for nine years, whereas Investment Y offers to pay you $8,000 per year for six years. Use
To compare the two investment options, we need to calculate their present values and assess which one yields a higher value.
Present value is a financial concept that takes into account the time value of money, meaning that money received in the future is worth less than money received today.
To calculate the present value of each investment, we will use the formula for the present value of an annuity:
PV = CF * ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value
CF = Cash Flow (the annual payment)
r = Interest rate per period
n = Number of periods
Investment X:
Cash Flow (CF) = $6,000
Interest rate (r) = ?
Number of periods (n) = 9
Investment Y:
Cash Flow (CF) = $8,000
Interest rate (r) = ?
Number of periods (n) = 6
Since we want to find out which investment has a higher present value, we need to calculate the interest rate. To do that, we can rearrange the formula and solve for r:
r = ((1 - (PV / CF)) ^ (-1/n)) - 1
Let's calculate the interest rate for each investment:
For Investment X:
PV = $6,000 * ((1 - (1 + r_X)^(-9)) / r_X)
For Investment Y:
PV = $8,000 * ((1 - (1 + r_Y)^(-6)) / r_Y)
We can use a trial and error method or use financial calculators, spreadsheets, or online present value calculators to find the interest rate for each investment.
Once we know the interest rates for both investments, we can compare the present values to determine which investment offers a higher value. The investment with the higher present value would be the better option.