Question

PART 2 - FINANCE

a) You purchase a house for $184,879.00. You made a down payment of $20,000 and the remainder of the purchase price was financed with a mortgage loan. The mortgage loan is a 30 year mortgage with an annual interest rate of 4.90%. Mortgage payments are made monthly. what is the monthly amount of your mortgage payment?

b) A 1,000 par value bond that pays interest annually just paid $116 in interest. What is the coupon rate?

c) An 8.76% coupon, 7-year annual bond is priced at $958.00. What is the current yield for this bond?

d) What is the price of a 1,000 par value semi-annual bond with 8 years to maturity and a coupon rate of 7.48% and a yield-to-maturity of 3.96%?

Answer 1

Part (A)

Formula for computing the EMI is = Loan amount/[{1-1/(1+r)^n}/r}

Where -

Loan amount = $(184,579 - 20,000) = $164,879

r = 4.9% p.a. i.e. 0.408333% monthly

n = 30 years i.e. 360 months

Computation = $164,879/[{1-1/(1+0.40833%)*360}/0.408333%]

EMI = $864.07

Note : The answer may vary due to rounding off.

Part (B) :

Coupon rate = Interest/Price of bond = $116/$1,000 = 11.6%

Part (C) :

Current yield = Next annual interest/Current price = (8.76%*$1,000)/$958 = 9.144%

Note - Face value of the bond is taken as $1,000

Part (D) :

Face value of bond = $1,000

Interest rate = 7.48% (3.74% semi-annually)

YTM is the rate at which present value of a bond is equal to it's current price.

YTM = 3.96% i.e. 7.92% annually.

PV of bond = (Interest + sale price of bond every year)/(1 + YTM)^(year)

= 74.8/(1+7.92%)^1 + 74.8/(1 + 7.92%)^2 + ...........+ (1000 + 74.8)/(1 + 7.92%)^8

= $974.64