Question

please answer all questions!!!

1. A loan may be repaid using the following two options of payments: i) Payments of 2,000 at the end of each year for eighteen years ii) Payments of 2,500 at the end of each year for nine years. Which of the following is closest to the effective annual interest rate being paid on the loan?

A. 14% B. 17%. C. 20%. D.23%. E. 26%

2. A loan is being repaid by payments of 1100 at the end of every 5 years over 55 years at a nominal annual interest rate of 4.4% compounded quarterly. Compute the loan amount.

A. 4092. B. 4150. C. 6504. D. 6931. E. 9432

3. The principal on a $12,000 loan is to be repaid within one year with level monthly payments, due at the beginning of each month. The twelve payments equal $1,000 each. The entire finance charge of $929 plus the first monthly payment are due immediately. Which of the following is closest to the effective annual interest rate on the loan?

A. 17.5% B. 18%. C. 18.5%. D.19%. E. 19.5%

4. Smith purchases a building by making a $10,000 down payment and agreeing to make eight semiannual payments of $2,500 each, the first due at the end of three years. The effective annual rate of interest is 5%.In which of the following ranges is the purchase price of the building?

Answer 1

Q1:

PV of 1st option of payment= 2000*[1-(1+r)^-18]/r

PV f 2nd option of payment= 2500*[1-(1+r)^-9]/r

These 2 option should be having same PV;

By trial and error; rate=17%

Q2:

quarterly rate=4.4/4=1.1% ;

rate every 5 year= (1+1.1%)^20-1 =.24458084 ----- 5 year payment

PV of loan=1100*[1-(1+.24458084)^-11]/.24458084 ------annuity formula; total 11 payments

=4092

Q3:

PV of loan=12000=1000*(1+r)*[1-(1+r)^-12]/r

By trail and error; 19.5%

Q4:

semi annula rate= (1+5%)^(1/2)-1 =.02469507659

PV of payments = 2500*[1-(1+.02469507659)^-8]/(.02469507659*(1+.02469507659)^6)

=15504.73

Total purchse price of building= 10000+15504.73 =25504.73