Theory of Interest- Non-annual interest rates and annuities
Find the annual effective rate of interest equivalent to a nominal rate of interest of 8% a year convertible semi-annually.
A. 8.16% B. 8.97% C. 9.05% D. 9.25% E. 9.5%
Calculate the accumulated value, at the end of 8 years, of payments of $4000 a year which are paid monthly at the start of each month. The annual effective rate of interest is 9%.
A. 26,236 B. 36,236 C. 46,236 D. 56,236 E. 66,236
Determine the annual effective interest rate that corresponds to a nominal rate of discount of 6% a year convertible quarterly.
A. 5.23% B. 6.23% C. 7.23% D. 8.23% E. 9.23%
Calculate the present value of payments of $1000 at the end of each year for the next 5 years. The nominal rate of discount is 10% a year convertible semi-annually.
A. 3330 B. 3415 C. 3600 D. 3715 E. 4000
Money is received at a rate of $6880 a year. Find the accumulated value at time 16 of the money received, given that payments are received at the end of every other year. The nominal rate of interest is 10% a year convertible every 6 months.
A. 230,250 B. 240,390 C. 250,420 D. 260,342 E. 270,358
Determine the present value of payments of $10 at the end of every month during the first year, $20 at the end of every month during the second year, $30 at the end of every month during the third year, and so on for 10 years. The nominal interest rate is 12% convertible monthly.
A. 3163 B. 3263 C. 3363 D. 3463 E. 3563
Olga buys a 5 year increasing annuity for $X. Olga will receives $2 at the end of the first month, $4 at the end of the second month, and for each month thereafter the payment increases by $2. The nominal interest rate is 9% convertible quarterly. Calculate X.
A. 2380 B. 2730 C. 2780 D. 2830 E. 2880
A sum of $100 is accumulated at a nominal rate of discount of 7.5% per year convertible quarterly for 1 year, and then at a nominal rate of interest of 7.5% per year convertible quarterly for 1 year. What is the accumulated amount of the investment after 2 years?
A. 110 B. 112 C. 114 D. 116 E. 118
The present value of a perpetuity of 6,500 paid at the end of each year plus the present value of a perpetuity of 8,500 paid at the end of every 5 years is equal to the present value of an annuity of k paid at the end of each year for 25 years. Interest is 6% convertible quarterly. Calculate k.
A. 10,340 B. 11,340 C. 12,340 D. 19,370 E. 19,560
A loan of 100,000 is to be repaid by 20 equal quarterly payments of X including principal and interest at a nominal interest rate of 6% per year compounded semiannually. The first payment is at the end of the first quarter. What is the X?
A. X < 5790 B. 5790 < X < 5800 C. 5800 < X < 5810
D. 5810 < X < 5820 E. X > 5820
Harry borrows $3500 from Mary. He agrees to repay the loan with annual payments, made at the end of each year, of $500, $1000, $1500, etc. with a smaller final payment one year after the last regular payment. Mary charges Harry a rate of discount of 10% convertible 4 times per year. Determine the amount of the final payment.
A. X < 1610 B. 1610 < X < 1640 C. 1640 < X < 1670
D. 1670 < X < 1700 E. X > 1700
Brian buys a 10-year decreasing annuity-immediate with annual payments of 10, 9, 8, ..., 1. On the same date, Jenny buys a perpetuity-immediate with annual payments. For the first 11 years, payments are 1, 2, 3, ..., 11. After year 11, payments remain constant at 11. At an annual effective interest rate of i, both annuities have a present value of X. Calculate X.
A. 26.6 B. 27.6 C. 28.6 D. 29.6 E. 30.6
Jane receives a 10-year increasing annuity-immediate paying 100 the first year and increasing by 100 each year thereafter. Mary receives a 10-year decreasing annuity-immediate paying X the first year and decreasing by X/10 each year thereafter. At an effective annual interest rate of 5%, both annuities have the same present value. Calculate X.
A. 860 B. 864 C. 868 D. 872 E. 876
Create a project group of no more than 6 people and e-mail the TA with the names and UNI of everyone in your group.