a) An investment gives you $10,000 from years 1 through 4 and 40,000 in year 5. If the interest rate is 7.5%, what is the present worth of this investment?
(2 points)
b)You need $150,000 to buy a new car in 5 years’ time. How much should you save at the end of every quarter for 5 years if a quarterly savings scheme offers you a rate of 8% p.a.?
1666.67
a) To find the present worth of the investment, we need to calculate the present value of the cash flows. The formula to calculate the present value of a future cash flow is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of years.
In this case, we have cash flows of $10,000 per year for 4 years and $40,000 in year 5. The interest rate is 7.5%. Let's calculate the present value of each cash flow and then sum them up.
Present value of $10,000 in year 1:
PV1 = $10,000 / (1 + 0.075)^1
Present value of $10,000 in year 2:
PV2 = $10,000 / (1 + 0.075)^2
Present value of $10,000 in year 3:
PV3 = $10,000 / (1 + 0.075)^3
Present value of $10,000 in year 4:
PV4 = $10,000 / (1 + 0.075)^4
Present value of $40,000 in year 5:
PV5 = $40,000 / (1 + 0.075)^5
Now, let's calculate the present worth of the investment:
Present worth = PV1 + PV2 + PV3 + PV4 + PV5
Finally, sum up the present values to get the present worth of the investment.
b) To find out how much you should save at the end of every quarter for 5 years, we can use the formula for the future value of a series of payments:
FV = P * ((1 + r)^n - 1) / r
Where FV is the desired future value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, we want to save $150,000 in 5 years, and the savings scheme offers a quarterly rate of 8%. Let's calculate the periodic payment required:
Periodic payment = FV / ((1 + r)^n - 1) / r
Substitute the values into the formula and calculate the periodic payment.