Question

Question 2

Kenny is planning for retirement in 20 years. Currently, he has $300,000 in a savings account and $600,000 in a mutual fund. Moreover, he plans to add to his savings by depositing $3,000 per month in his savings account at the beginning of each month for the next twenty years until retirement. The savings account will return 5% APR compounded monthly and the investment in the mutual fund will return 8% compounded annually.

(a) How much money will Kenny have at retirement 20 years later? (b)





(c)
Kenny expects to live for 20 years after he retires and at retirement he will deposit all of his savings in a bank account paying 2% APR compounded monthly. If he wants to withdraw an equal sum of money at the end of each month from the bank account for financing his daily expenses after retirement, how much can he withdraw each time?

If the yield to maturity of a bond is higher than its coupon rate, the par value of the bond should be higher than its price, resulting in a discount bond. Conversely, if the yield to maturity of a bond is lower than its coupon rate, the par value of the bond should be lower than its price, resulting in a premium bond. Critically discuss this phenomenon. (word limit: 150 words)

Answer 1

a]
1]	FV of amount in savings at t0 = 300000*(1+0.05/12)^240 =	$     8,13,792.09
	FV of amount in mutual fund at t0 = 600000*(1+0.08/12)^240 =	$ 29,56,081.66
	FV of annual deposit in savings account [annuity due] = 3000*(1+0.05/12)*((1+0.05/12)^240-1)/((0.05/12) =	$ 12,38,238.93
	Money at retirement	$ 50,08,112.67
b]	Amount that can be withdrawn every month is an annuity, whose PV would be $5008112.67.
	Adapting the formula for finding PV of annuity, the monthly sum that can be withdrawn = 5008112.67*(0.02/12)*(1+0.02/12)^240/((1+0.02/12)^240-1) =	$        25,335.21
	BOND INTEREST RATE & PRICE:
	A bond's price is the PV of the expected cash flows from the bond, if, it is held till maturity, the discount rate being the market interest rate [not the coupon rate]
	The expected cash flows are the maturity value,
	which, is, generally, the par value and the periodic
	interest payaments.
	When the market interest rate is more than the
	coupon rate the result of discounting the expected
	cash flows would be a PV less than the face value.
	The bond would then be at a discount.
	Conversely, when the market interest rate is less
	then the coupon rate, the price will be more than
	the face value and the bond would be at a premium.
	Thus, the price of bond would move inversely with
	the movement in market interest rate.
	The assumption here is that the intervening cash
	flows, that is the coupon payments, can be
	reinvested at the market rate. Such an assumption
	is not true as, the market rate would keep on
	changing. At its extreme situation, a bond that was
	a premium bond could become a discount bond on a
	change in market interest rate and vice versa, over a
	period of time.
	Hence, investments in bonds are subject to price
	risk and reinvestment rate risk, which should be
	born in mind.