Question

Which of the following is NOT correct? Multiple Choice Other things being equal, the more frequent the compouding period, the higher the APR. 0 The arguement that 900 dollars today worth more than 900 dollars one year from now is correct only when interest rate is positive. 0 Cash flows occuring in different periods should not be compared unless the flows have been discounted to a common date. 0 Other things being equal, the more frequent the compouding period, the higher the EAR

Answer 1

i). Ans- Option A.

Correct Statement is -Other things being equal, the higher the compounding period the higher the EAR.

APR is annual rate which is same, while EAR is Effective annual rate which is computed by compounding the interest rate with the no of compounding periods.

ii). Present value of future semi-annual annuity payments = $84000

Calculate the Effective Interest rate using IRR Technique in Present Value of annuity formula:

PresentValue = C* [1 – (1 + r)-ny

Where, C= Periodic Payments = $9000

r = Periodic Interest rate

n= no of periods= 10*2 =20

Taking r = 17%

Periodic rate = 0.17/2 = 0.085

Present alue = 9000 * [1 – (1 + 0.085) -20 0.085

Present Value - 9000 - 11 -0.195616391 0.085

Present Value = $ 85170.03

now, taking r = 19%

periodic r = 0.19/2 = 0.095

Present alue = 9000 * [1 – (1 + 0.095) -20 0.095

PresentValue = 9000 * 1 [1 -0.1628237] 0.095

Present Value = $ 79311.44

Finally, calculating r:

r = Lower Rate + Lower Rate) PresentValueLR - PresentValue -* (Higher Rate - PresentValueLR – PresentV aluehr

r = 17+ 85170.03 - 84000 - * (19 – 17) 85170.03 – 79311.44

r = 17.40%

Hence, Option C . 17.38% (with IRR technique interest rate comes to be approx.)

iii) Calculating the no of years it take to become amount triple:

FutureValue = Invested Amount(1+r)"

where, Invested amount = $500

r = Periodic Interest rate = 0.06

n= no of periods

Future Value = $1500

1500 = 500(1+0.06)ⁿ

3 = (1.06)ⁿ

taking log both sides,

log(3) = nlog(1.06)

0.47712125= n(0.02530587)

n = 18.85 years.

Hence, Option D. 18.85 years

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