1.) What is the present value of $1,500 received for 24 months in arrears, follo

Question

1.)

What is the present value of $1,500 received for 24 months in arrears, followed by $1,200 received for 36 months in arrears, if the annual discount rate appropriate is 9.25%?

$62,261

$13,984

$15,764

$64,022

2.)

What investment accumulates more interest--15% compounded semiannually, or 14% compounded daily?

The 15% option earns one percentage point more than the 14% option over a year

The 15% option accumulates more over a year--EAR of 15.5% vs. the 14% option, with an EAR of 15.0%

They accumulate the same amount over a year

The 14% option earns an EAR of 15% and is better than the 15% option with an EAR of 15.9%

$62,261

$13,984

$15,764

$64,022

Explanation / Answer

1)

Present value of ordinary annuity PV

= C * [1 - (1+i)^-n]/i

Present value of 1500 recieved for 24months at 9.25%

i = interest rate per period = APR/number of periods in a year = 9.25%/12

C= payment per month = 1500

n = number of periods =24

PV1 = 1500 * [1 - (1+9.25%/12)^-24]/9.25%/12

= $32751.43 ...............................ans

Present value of 1200 recieved for 36months at 9.25%

i = interest rate per period = APR/number of periods in a year = 9.25%/12

C= payment per month = 1500

n = number of periods =24

PV at the end of 24 months = 1200 * [1 - (1+9.25%/12)^-36]/9.25%/12

= 37598.44499

PV at present PV2= 37598.44499/(1+9.25%/12)^24 = 31270.40

total present value = PV2 + PV1

= 32751.43 + 37598.45

= 64022

Hence d)$64022 is the answer

2)

Equivivent anual rate EAR = (1+ Annual percentage rate/number of preiods ina year)^number of periods in a year -1

so , 15% compounded semi annually

EAR = (1+ 15%/2)^2 - 1 = 15.5625%= 15.5% (approxmately)

14% compounded daily and assuming 365 days a year

EAR = (1+14%/365)^365 -1 = 15.0243% = 15% ( approxmately)

therefore

b.  
The 15% option accumulates more over a year--EAR of 15.5% vs. the 14% option, with an EAR of 15.0%

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