A security will make payments of $25 per month, plus $1000 at maturity. The price of...

A security will make payments of $25 per month, plus $1000 at maturity. The price of this security is $2000. Which of the following is true? If the time to maturity is 7 years then the effective rate is 10.52%% If the time to maturity is 4 years then the effective rate is 10.52% If the time to maturity is 7 years then the effective rate is 10.05% If the time to maturity is 4 years then the yield to maturity is 10.05% If the time to maturity is 7 years then the effective rate is 3.34%

Solutions

Expert Solution

Face value of the security = $1000

Monthly coupon payment = $25

Therefore, monthly coupon rate = 25/1000 = 2.5%

Present value of the security = $2000

We see that in options there are two cases. In the first case, the time to maturity is 7 years and in second case the time to maturity is 4 years. We will calculate the effective rate for both the cases

Case I: time to maturity = 7 years

Sine the security pays monthly coupon payments with a monthly coupon rate = 2.5%

No. of periods of coupon payment = 7*12 = 84 months

We can calculate the monthly rate using a financial calculator or an excel

Method 1: Using ba ii plus calculator

N = 84, PV = -2000, PMT = 25, FV = 1000

CPT -> I/Y

we get I/Y = 0.837374721%

This is the monthly rate, effective annual rate can be calculated using the below formula

EAR = (1+0.837374721%)¹² - 1 = 10.5244505770738%

Method 2: Using Excel

We will use the RATE function in Excel to calculate the monthly rate

nper = 84, pmt = 25, pv = -2000, fv = 1000

=RATE(84,25,-2000,1000) = 0.837374721%

Effective annual rate = EAR = (1+0.837374721%)¹² - 1 = 10.5244505770738%

Hence, the first option i.e., If the time to maturity is 7 years then the effective rate is 10.52% is true

Answer -> If the time to maturity is 7 years then the effective rate is 10.52%

jeff jeffy answered 3 weeks ago

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