Math 2620, Spring 2022, Test #2
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Math 2620, Spring 2022, Test #2
1. What is the present value at time 0 (to the nearest dollar) of a 10 year annual pay geometrically increasing annuity immediate which increases by 3% each year if the first payment is $100? Assume the nominal annual interest rate convertible semi-annually equals 6% .
A . $ 828
B. $ 842
C. $ 855
D. $ 867
E. None of the above
2. For i=5% and n=5, what is the ratio of (
)
to (
) 
?
A . .984
B. 1.0237
C. 1.067
D. 1.081
3. Given a nominal annual interest rate of 8% convertible quarterly, what is the biennial effective interest rate?
A . About 13.6 %
B. About 14.9 %
C. About 15.5%
D. About 16.4%
E. About 17.2%
4. What is the accumulated value at year 10 (to the nearest dollar) of a payment of $1,000 at year 4 assuming a nominal rate of discount of 6% convertible monthly?
A . $1,359
B. $1,376
C. $1,401
D. $1,435
E. $1,467
5. At some given rate of interest, i ≠ e and i > 0, and some starting amount $X for each, what must be the ratio of the accumulated value of a 10-year compound increasing annuity due that increases by e% each year to the present value of a 10-year compound increasing annuity immediate that also increases by e% each year?
A . (1 + 
)9 / (1+e)
B. (1 + 
)10 / (1+e)
C. (1 + 
)11 / (1+e)
D. (1 + 
)10 / (i-e)
E. (1 + 
)11
6. What is the present value (at time zero) of a continuous payment stream paid at an annual rate of payment = 50 exp (- .02t) from t= end of year 2 to end of year 6 given a force of interest of 5%?
A . $ 131.43
B. $ 142.20
C. $ 151.65
D. $ 165.88
E. $ 179.21
7. Drew receives $600 dollars at the end of year 1, $520 at the end of year 2, followed by similar annual decreases up to a final payment amount of $200. What is the accumulated value of these payments at the time of the final payment (to the nearest dollar) when the effective annual interest rate is 8%?
A . $2,659
B. $2,831
C. $3,066
D. $3,298
E. None of the above
8. An annuity provides payments annually of $40 at time 1 year, then increasing by $20 each year up to a payment of $220. The annual effective interest rate is 20%. What is the present value of the annuity to the nearest dollar?
A . $ 375
B. $ 389
C. $ 402
D. $ 413
E. $ 425
9. Find the accumulated value of quarterly payments of $75 made at the beginning of every 3 months for 5 years when the nominal annual interest rate convertible semi-annually is 10% .
A . $1, 146.83
B. $1,181.67
C. $1,201.52
D. $1,227.18
E. $1,242.41
10. A payment of $10 is to be made at the beginning of year 10. Assuming a biennial effective interest rate of 21%, what is the present value of that payment at time 0?
A . $ 3.86
B. $ 4.07
C. $ 4.15
D. $ 4.24
E. $ 4.31
11. Payments of $50 are made at the end of years 1, 3, 5, 7. Payments of $80 are made at the end of years 2, 4, 6, 8. Determine the accumulated value of the entire set of payments at time 8 (to the nearest dollar) if the nominal rate of discount convertible monthly is 12% .
A . $755
B. $774
C. $791
D. $812
E. $830
12. Jim invests $5,000 into a fund earning a nominal annual discount rate of 8% convertible quarterly . Determine the amount of interest earned on Jim’s funds in the last 6 months of the third year of his investment (to the nearest dollar) .
A . $243
B. $252
C. $264
D. $276
E. None of the above
13. If Mark pays the fair price of $200 for a perpetuity which pays $8/year at the end of each year, what is the equivalent nominal annual discount rate convertible biannually ?
A . 3.88 %
B. 3.92 %
C. 3.96 %
D. 4.00 %
E. 4.05 %
14. Ian, Doug, and Ellie each receive annual payments at the start of each year for 20 years. Ian’s payments start at $2 in year 1 and increase by $2 each year up to a final payment of $40. Doug’s payments start at $40 in year 1 and decrease by $2 each year to a final payment of $2. Ellie receives level payments of $10 per year. If the sum of their present values at time zero is $600.09, what is the approximate value of the interest rate i?
A . 6.32 %
B. 6.74 %
C. 7.08 %
D. 7.26 %
E. 7.52 %
15. Assuming a constant force of interest, δ = .03, what is the present value of a continuous series of payments with each payment at time t = 2t+4, paid from time 0 to time 6 (to the nearest dollar)?
A . $ 42
B. $ 46
C. $ 50
D. $ 54
E. $ 58
16. Determine the accumulated value at the end of the last year of payments (to the nearest dollar) of the following amounts that are paid continuously over each year. The annual amount is $15 during the first year, $30 during the second year, $45 during the third year, and so on, up to the last annual amount of $90. The annual effective interest rate is 5%?
A . $262
B. $315
C. $351
D. $406
E. None of the above
17. Judy and Luke each receive ten annual payments where the payments begin at $P per year but increase by 4% each year. Judy receives her first payment at the end of this year, while Luke’s payments start today. If the ratio of Luke’s present value of all payments to Judy’s present value of all payments is 1.1024, which of the following most closely approximates the accumulated value of Luke’s payments at the time he receives his last payment?
A . $ 13P
B. $ 15P
C. $ 17P
D. $ 19P
E. $ 21P
18. If the annual effective interest rate, i, equals 8%, determine the ratio of 
) to 
.
A . 0.98
B. 1.02
C. 1.04
D. 1.06
E. 1.08
19. Jill receives a 5-year increasing annuity- immediate paying $50 the first year and increasing by
$50 each year thereafter. Mark receives a 5-year decreasing annuity- immediate paying X the first year and decreasing by X/5 each year thereafter. At an annual effective interest rate of 10%, both annuities have the same present value . Calculate X to the nearest dollar.
A . $204
B. $220
C. $238
D. $253
E. $275
20. Given a nominal annual rate of interest of 9% compounded biennially, how much does $1000 grow to in four years?
A . $1,312.26
B. $1,355.60
C. $1,392.40
D. $1,427.62
E. $1,442.52
2022-05-03