Question

2. Lauren deposits $250 into her retirement account at the end of each month. She plans on making monthly contributions for 20 years. If her account earns a 5.62 percent annual interest rate, what percent of the total, at the end of 20 years, are her out-of-pocket contributions?
A. less than 49.2
B. more than 49.2 percent but less than 50.8 percent
C. more than 50.8 percent but less than 52.4 percent
D. more than 52.4 percent but less than 54.0 percent
E. more than 54.0 percent

3. What is the future value of an annual $1,825 annuity due over 12 years if the interest rate is 4.48 percent?
A. less than $28,700
B. more than $28,700 but less than $29,325
C. more than $29,325 but less than $29,950
D. more than $29,950 but less than $30,575
E. more than $30,575

4. Elmers Almonds, Inc. wants to buy a storage facility for $370,000 with terms of 20 percent down and the balance to be paid off over 25 years at a 5.85 percent rate of interest on the unpaid balance. What are the 25 equal annual payments that Elmers Almonds must pay?
A. more than $22,375
B. less than $22,375 but more than $21,720
C. less than $21,720 but more than $21,065
D. less than $21,065 but more than $20,410
E. less than $20,410

5. What is the interest rate of an 8-year, monthly $875 annuity with a present value of $58,375?

A. less than 8.75 percent
B. more than 8.75 percent but less than 9.60 percent
C. more than 9.60 percent but less than 10.45 percent
D. more than 10.45 percent but less than 11.20 percent
E. more than 11.20 percent

Answer 1

2)

Future value = payment per period * [(1+i)^n - 1]/i

i = interest rate

n = number of periods

Future value = 250 * [(1+(0.0562/12))^240 - 1]/(0.0562/12)

= 110448.83

Percentage of her contributions = (250*240)/110448.83 =54.32%

Hence choose E)

3)

Future value of annuity due = payment per period * [(1+i)^n - 1]/i * (1+i)

i = interest rate

n = number of periods

= 1825 * [(1+4.48%)^12 - 1]/4.48%

= 28189.35

4)

Loan amount = Present value of future monthly payments = monthly payment * [1-(1+i)^-n]/i

i = interest rate per period

n = number of periods

Loan amount = 370000 * 0.8 = 296000

x * [1 - (1+5.85%)^-300]/5.85% = 296000

annual payment = 17316

5)

present value of annuity = payment * [1-(1+i)^-n]/i

=>

interest rate = RATE(number_of_periods, payment_per_period, present_value, [future_value], [end_or_beginning], [rate_guess])

= RATE(96,875,-58375,0) * 12

= 9.65%

hence choose C)