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2 years ago

Compounding

Business

1 answer:

r-ruslan [8.4K]2 years ago

6 0

Answer:

Task A:

<u>What is the effecting annual rate changed on this loan?</u>

Answer is 3.03%

<u>What would be the quarterly payment on this loan?</u>

Answer is $5,403.06

<u>Dr. Zoidberg also discovers that instead of the special promotional rate he can make an additional down payment of $20,000 that would lower his loan amount accordingly (i.e. by $20,000). At what APR would Dr. Zoidberg have the same quarterly payment with this option as with the initial promotional rate of 3%?</u>

Answer is 12.21%

<u>Dr. Zoidberg finds that he can get 1.5% APR if he elects option (c). What will his quarterly payment be under this option?</u>

The answer is $4,159.37

<u>Now assume that that payment frequency changes to annual, preserving the same EAR. What is his payment now?</u>

The answer is $21,835.46

Explanation:

<h2>Task A: </h2><h3>What is the effecting annual rate changed on this loan?</h3>

Solution:

Effective annual rate = (1 + (APR/n))ⁿ - 1

where

n = number of compounding periods per year = 4 (compounding quarterly)

APR = 3%

Effective annual rate = (1 + (3%/4))⁴ - 1

Effective annual rate = 3.03% (answer).

<h2>Task B: </h2><h3>What would be the quarterly payment on this loan?</h3>

Solution:

Quarterly loan payment is calculated using PMT function in Excel :

Rate = 3% / 4 (converting annual rate into Quarterly rate)

nper = 5*4 (5 year loan with 12 Quarterly payments each year)

pv = 100000 (loan amount)

PMT Formula = PMT(3%/4,5*4,100000)

PMT is calculated to be $5,403.06 (answer)

Note: PMT calculation has been attached.

<h2>Task C:</h2><h3>Dr. Zoidberg also discovers that instead of the special promotional rate he can make an additional down payment of $20,000 that would lower his loan amount accordingly (i.e. by $20,000). At what APR would Dr. Zoidberg have the same quarterly payment with this option as with the initial promotional rate of 3%?</h3>

Solution

The quarterly rate to have the same quarterly payment is calculated using RATE function in Excel :

nper = 5*4 (5 year loan with 12 Quarterly payments each year)

pmt = -5403.06 (Quarterly payment. This is entered with a negative sign because it is a payment)

pv = 80000 (loan amount)

RATE is calculated to be 3.05%. This is the quarterly rate. To get APR, we multiply by 4.

Formula for APR = RATE(5*4,C1,80000)*4

APR = 12.21% (answer)

<h2>Task D</h2><h3>Dr. Zoidberg finds that he can get 1.5% APR if he elects option (c). What will his quarterly payment be under this option?</h3>

Solution:

Quarterly loan payment is calculated using PMT function in Excel :

rate = 1.5% / 4 (converting annual rate into Quarterly rate)

nper = 5*4 (5 year loan with 12 Quarterly payments each year)

pv = 80000 (loan amount)

PMT formula: PMT(1.5%/4,5*4,80000)

PMT is calculated to be $4,159.37

<h2>Task E</h2><h3>Now assume that that payment frequency changes to annual, preserving the same EAR. What is his payment now?</h3>

Solution:

PMT = PMT(3%,5,100000)

PMT = $21,835.46

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