Which of the following statements is/are correct regarding an annual rate of 6%?

Question

Which of the following statements is/are correct regarding an annual rate of 6%? a. Its EFF (or EAR) is larger than 6%, if the rate is semi-annually compounding. b. Its EFF (or EAR) is same as 696, if the rate is annually compounding. C. Its periodic rate is larger than 3%, if the rate is semi-annually compounding. d. Both a and b are correct e. Both a and c are correct. A bank recently loaned you $450,000 to buy a house. The loan is for fifteen years and is fully amortized. The nominal rate on the loan is 3%, and payments are made at the end of each month. What will be the remaining balance on the loan after you make the 130th payment? a. $148,125.07 b. $138,363.22 c. $145,890.73 d. $148,532.38 e. $147,599.03

Explanation / Answer

1. Effective Annual rate if 6% is compunded semi annualy = (1+r)^n-1

here r=6/2= 3% and n =2

EAR= (1.03^2-1)= 1.061-1= 6.1% .

And Effective Annual rate if 6% is compunded annualy = (1+r)^n-1

here r=6% and n =1

EAR= (1.03^1-1)= 1.06-1= 6%

Hence A and B both are correct. Option D

2. Remaining Balance= Present value of remaining PMT

Here R=3/12 =0.25% as it it compounded monthly

Initial loan value= $450000

n = 15*12= 180 as it s componded monthly

so first we need to calculate PMT= r*Initial loan value/(1-(1+r)^-n)

PMT=(0.0025*450000)/(1-(1.0025^-180))

=1125/(1-0.6380) =1125/0.362= $3107.62

Now we need to calculate the PV of remaining 50 installment

PV=PMT*((1-(1+r)^-n)/r)

=3107.62*((1-0.8826)/0.0025)= 3107.62*(0.117/0.0025)

= $145890.73, Hence Option c is correct

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