Question

Please use a calculator for the following problems and please show work

1) Brianne plans to deposit $100,000 today into a fund that will be needed at the end of 6 years. She will receive 12% interest on the fund balance. What is the fund balance at the end of year 6 assuming semiannually compounding

2) What is the present value of $10,000 to be received each year for 20 years if the payments start immediately. Assume a discount rate of 4%

3) Robert wants to withdraw $100,000 a year for 30 years after he retires. He will probably work for 30 years and earn 4% interest during the whole time. How much does Robert have to contribute to her pension fund each year so she can retire on $100,000 a year

Answer 1

The answer has been presented in the supporting sheet. All the parts has been solved with detailed explanation and format. For detailed answer refer to the supporting sheet.

2 3 4 5 Answer Part 1) Future value = amount invested*(1+i)an = 100000*(1+(12%/2)^(6*2) = $201219.65 (rounded off to 2 decimal places) 7 Thus the correct answer is $201219.65 Part 2) LO Present value = annual payment*Present value annuity (20,4%) -1 = 10000*((1-(1.04)^-(20-1))/.04)+1) -2 = 10000*14.13394 -3 141339.4 5 Thus the correct answer is $ 141339.39 -7 Part 3) 9 Present value of $ 100000 after he retires 0 = amount per year*((1-(1+i)^-n)/i) 1 = 100000*((1-(1.04)^-30)/.04) 2 = 100000*17.292033 -3 = 1729203.3 5 Amount in pension fund when he retires = annual contribution *((1+i)^n-1)/i) 6 1729203.3 = annual contribution *((1.04)^30-1)/.04) 7 1729203.3 = annual contribution * 56.084938 8 1729203.3/56.084938 = annual contribution -9 30831.87 = annual contribution 1 Thus the correct answer is $ 30831.87