Question

You want to buy a house 5 years from now, and you plan to save $4100 per year. beginning Immediately. You will make 5 deposits in an account that pays 4.3% interest. Under these assumptions, how much will you have 5 years from today?

Company XYZ soustanding bonds have a $1.000 value and they mature in 25 years. Their nominal yield to maturity is 9.66 % they pay interest semiannually, and they sell at a price of $850. What is the bond's annual coupon interest rate?

Answer 1

Q1. Future Value of an Anuuity Due: Future value of an annuity is the sum of future value of each payment or deposits made during the period. When the first payment made today or immediately (at the begining of each period) it is called future value annuity due or annuity immediate. It is formulated by :

Here: A is the constant periodic flow i.e. $4,100

r is the interest rate per period i.e. 4.3%

n is the duration of period i.e. 5 years

Therefore:

approx.

Therefore answer is $23,300.70

Q2. Finding Annual Coupon Rate of a Bond

Step: 1. We have been given:

Face Value/Redemption Amount = $1,000,

Number of periods (n) = 25 years

=> 50 periods,

Yield to maturitty (YTM) = 9.66% p.a.

=> 4.83% per 6 months

Price of the bond at Y₀ = $850

Annual Coupon Amount    = x (assumed)

=> 0.5x

Step: 2. Price of the bond

P₀ = Coupon Amount * PVAF(r,n) + Redemption Amount * PVIF(r,n)

Here: PVAF is the Present Value of Annuity Factor,

r is the yield to maturity i.e. 4.83%,

n is the years to maturity i.e. 50 periods,

PVIF is the Present Value Interest Factor

Step: 3. Coupon Amount of the bond.

850 = 0.5x * PVAF(4.83%,50) + 1,000 * PVIF(4.83%,50)

850 = 0.5x * 18.7461 + 1,000 * 0.0946

850 = 9.3731x + 94.6

9.3731x = 850 - 94.6

9.3731x = 755.4

x = 755.4/9.3731

x = 80.59

Step: 4. Coupon Rate = Coupon Amount / Face Value of the Bond * 100

= 80.59 / 1,000 * 100

= 8.059% approx.

Therefore answer is 8.059%.

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