An investor has $85,000 in a bank account at 6% interest compounded annually. They can use this sum to pay for the purchase of a plot of land. They expect that in 10 years they will be able to sell the land for $155,000. During that period they will have to pay $3,000 a year in property taxes and insurance. Should they make the purchase based on a rate of return analysis?
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To determine whether the investor should make the purchase based on a rate of return analysis, we need to calculate the future value of their investment at the end of 10 years and compare it to the cost of the land and expenses.
The formula for calculating the future value of an investment with compound interest is:
FV = PV * (1 + r)^n
Where:
FV = future value
PV = present value
r = interest rate
n = number of compounding periods
Given:
PV = $85,000
r = 6% = 0.06
n = 10 years
Calculating the future value of the investment:
FV = $85,000 * (1 + 0.06)^10
FV = $85,000 * (1.06)^10
FV = $85,000 * 1.790847
FV ≈ $152,043.95
Therefore, after 10 years, the investment would have a future value of approximately $152,043.95.
While the plot of land is expected to sell for $155,000, the investor will have to pay $3,000 per year in property taxes and insurance for 10 years:
Total expenses = $3,000 * 10
Total expenses = $30,000
Therefore, the investor's net profit from the sale of the land would be:
Net profit = $155,000 - $30,000
Net profit = $125,000
Considering the net profit from the sale and the future value of the investment, it seems like a reasonable decision to go ahead with the purchase. However, other factors like property market trends, potential additional costs, and the investor's risk tolerance should also be taken into account before making a final decision.
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