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amm1812
3 years ago
8

The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the presen

t and future values of cash flows. An investor can invest money with a particular bank and earn a stated interest rate of 4.40%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?
Interest Rates
Nominal rate 4.40%
Periodic rate 1.10%
Effective annual rate 4.47%
Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 4%. But the bank is compounding daily. What is the effective interest rate that Rahul would pay for the loan?
a. 4.081%
b. 4.202%
c. 3.959%
d. 4.395%
Another bank is also offering favorable terms, so Rahul decides to take a loan of $22,000 from this bank. He signs the loan contract at 9% compounded daily for nine months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)
a. $24,477.81
b. $24,948.54
c. $23,536.36
d. $24,007.09
Business
1 answer:
Anastasy [175]3 years ago
3 0

Answer:

1. a. 4.081%

2. c. $23,536.36

Explanation:

1. Periodic rate=(4.4%/4) = 1.1%

EAR=(1+APR/m)^m-1

where m=compounding periods

= (1+0.044/4)^4-1

= 1.011^4 - 1

= 1.04473133864 - 1

= 0.04473133864

= 4.47%

EAR=(1+APR/m)^m-1

where m=compounding periods

=(1+0.04/365)^365-1

= (1+0.00010958904)^365 - 1

= 1.00010958904^365 - 1

= 1.04080849272 - 1

= 0.04080849272

= 4.081%

2. A=P(1+r/365)^365*n

where  A=future value, P=present value, r=rate of interest, n=time period.

= 22000*(1+9%/365)^(9/12*365)

= $23,536.36

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Answer:

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                                          <u>Cash Budget</u>

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Cash outflows:                     (<u>$28,000) </u>    (<u>$30,000)</u>       (<u>$22,000)</u>

Monthly cash flow:                ($8,000)       ($4,000)          $18,000          

Monthly interests:                           $0             ($76)          ($116.76)

Initial cash balance:                <u>$8,400 </u>       <u> $8,000 </u>         <u> $8,000</u>

Ending cash balance:                $400          $3,924       $25,883.24

Required bank loan:               $7,600          $4,076                   $0

Payment of bank loan:           <u>        $0  </u>        <u>       $0  </u>       <u>  ($11,676)</u>

Total                                         $8,000         $8,000       $14,207.24           

Explanation:

A cash budget is the estimation of the business's future cash flows including estimated revenues and expenses.

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Answer:

Account Title                                  Debits                       Credits  

Cash                                                 34,900    

Accounts receivable                         42,600    

Supplies                                               860    

Inventory                                            62,600    

Notes receivable                              22,600    

Interest receivable                              1,507    

Prepaid rent                                         1,150    

Prepaid insurance                                 2,150    

Office equipment                                90,400    

Accumulated depreciation                                                45,200  

Accounts payable                                                               33,600  

Salaries payable                                                                   1,400  

Notes payable                                                                   52,600  

Interest payable                                                                  1,578  

Deferred sales revenue                                                        3,300  

Common stock                                                                   78,200  

Retained earnings                                                              35,000  

Dividends                                              6,600    

Sales revenue                                                                      159,000  

Interest revenue                                                                      1,507  

Cost of goods sold                                  83,000    

Salaries expense                                     21,600    

Rent expense                                          13,450    

Depreciation expense                             11,300    

Interest expense                                      1,578    

Supplies expense                                     4,340    

Insurance expense                                    6,450    

Advertising expense                                  4,300    

Totals                                                          411,385                  411,385

Insurance expense

= 8,600 * 9/12 months = $6,450

Prepaid Insurance = 8.600 - 6,450 = $2,150

Supplies expense = 2,400 + (2,800 - 860) = $4,340

Interest expense and Interest payable = 12% * 3/12 * 52,600 = $1,578

Rent = 12,300 + 1,150 = $13,450

Interest revenue = 22,600 + 8% * 10/12 months = $ 1,507

Accumulated depreciation = 33,900 + 11,300 = $45,200

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