Question

If the time value of the money is .10 how much do you have to save per year for 20 years to have $50,000 per year for perpetuity? Assume that the first deposit is immediate and that the first payment will be at the beginning of the 21^st year.

Suppose that you decide to hold the bonds in the previous question for a year, and then sell them. The next year, the interest rate on comparable bonds increases to 9.5%. How much will you be able to sell them for at that time? If you received a 5% rate of return on your money and you stick the coupons in the bank, in retrospect, would you have been better off selling the bonds when you first got them, or, holding them for a year, and selling them at the higher yield (9.5%)? Solve with Excel

Answer 1

Amount of money you need to have by year 20 = Annual Payment / Interest rate = 50,000 / 10% = $500,000

Now, annual saving can be calculated using PMT function on a calculator with BEGIN mode.

N = 20, I/Y = 10%, PV = 0, FV = 500,000 => Compute PMT = $7,936.19 should be your annual savings.

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Value of the bond can be calculated using PV function on a calculator

N = 5, I/Y = 8.7%, PMT = 10% x 100,000 = 10,000, FV = 100,000

=> Compute PV = $105,096.15 is the price of a the bond a year earlier.

Today, I/Y = 9.5%, N = 4 => Compute PV = $101,602.24 is the bond price today.

But you would also receive $10,000 in coupon, and hence the total value of the bond today = $111,602.24

Hence, your returns = 111,602.24 / 105,096.15 - 1 = 6.19% > 5%

As the bond price declined in the last one year but your total returns are still higher than 5% and hence, you are better to hold them for a year.