A ninterest rste stated .. nominal t2% per year compounded quarterly i, ehe same

Question

A ninterest rste stated .. nominal t2% per year compounded quarterly i, ehe same " A) eflective 1%per menh. Bonnal 1% per month. 3%pef quarter. H) D) Question 2 12.68% per year. An interest rate of 12% per year compounded continuously is the same as A) 1% per month compounded continuously. Effective 12.683% per year compounded continuously. D) None of the above Questlon 24 If you deposit $1000 per month into an account which pays interest at arate of 12% per year compounded monthly, the amount of money you would have at the end of five years is nearest to A) $6,353 B) $68,321 D) $81,670 Question 25 The owner of a small business borrowed $70,000 with an agreement to repay the loan with quarterly payments over a five year time period if the interest rate is 12% per year compounded quarterly, his loan payment each quarter is nearest to: A) $2.605 B) $5,864 C $9,372 D) $19,419 Question 26 A metal plating company wants to set aside money now to prepare for a lawsuit it expects to face in four years. If the company wants to have $1 lump sum if the account will earn 1% per month? ,000,000 available at that time, how much must it set aside now in one A) $620,300 B) $711,800 C) $836,400 D) $961,000 Problems 27 through 29 are based on the following statement: A small manufacturing company expects to have to replace its aging production line in five years with new equipment. The current equipment has operating costs which are expected to be $5,000 this year, $6,000 next year, with costs increasing by $1,000 per year through year five. The equipment will have a salvage value of $30,000 at the end of year five. The new equipment is expected to cost $150,000 and the company uses an intrest rate of 16% per year compounded quarterly on its investments.

Explanation / Answer

22.

C

Working note:

If nominal interest rate is 12% per year compounded quarterly, then:

Effective annual interest rate = (1+12%/4)^4 -1 = 12.55%, so alternative d is incorrect.

Alternative b is incorrect as 12% nominal rate (compounded quarterly) will have more than 1% nominal monthly interest rate.

Alternative C is correct as 12% per year compounded quarterly is equivalent to 3% rate per quarter.

3% rate per quarter. = (1.03)^4 -1 = 12.55 % effective annual rate

23.

A

Working note:

Effective annual interest rate = 2.7182^.12*1 - 1 = 12.75%

As per the alternative A, Effective annual interest rate =2.7182*(.01*12) – 1 = 12.75%

So, alternative A is correct.

24.

D

Working Note:

Future value at the end of 5 years = 1000*((1+1%)^60 -1)/.01 = $81669.67 or $81670

25.

B

Working note:

Quarterly interest rate = 12%/4 = 3%

Time = 20 quarters

Loan amount = $70000

Quarterly installment = 70000/((1-1/1.03^20)/.03) = $4705

26.

A

Working note:

Time = 48 months

R = 1% per month

Amount in lump sum = 1000000/(1+1%)^48 = $620260.41

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