19)
Volunteer Pharmaceuticals (VP) wants to set aside money in the R&D fund to seek
supplemental drug applications of its two newly developed drugs. Instead of putting
away $780 million now, VP plans to set aside $A each year from year 1 through 40. What
should the value of A be if VP expects to earn 7% per year for the first 5 years and 2% per
year for the remaining years?
19)
Answer:
$35,577,124.82
Explanation:
Find the present worth of the annual contributions to the R&D fund. Because of
the varying interest rates, we need to find the present worth of the contributions
from year 6 to year 40 at the end of year 5 with the rate of 2%, before moving to
year 0 with P/F factor at the rate of 7%.
P = A (P/A, 7%, 5) + A (P/A, 2%, 35)(P/F, 7%, 5)
= A (4.1002) + A (17.8240)
Equate the present worth to $780,000,000 and solve for A.
P =$780,000,000 = A (4.1002 )+ A (17.8240)
Thus, A =$35,577,124.82
20)
How much must be deposited each month for 8 months at an interest rate of 5% per month
to allow for a single withdrawal of $44,500 at the same time as the last deposit?
20)
Answer:
$4659.15
Explanation:
Find the uniform annual deposits with an A/F factor.
A =$44,500 (A/F, 5%, 8)
=$4659.15
21)
What is the amount of equal annual deposits needed in years 7 through 14 to provide for a
series of annual withdrawals of $2400 beginning 9 years from now and increasing at the
rate of 2% per year through year 19? Assume an interest rate of 5% per year.
21)
Answer:
$3064.71
Explanation:
Find present worth of the withdrawals at time 8 and bring it back to t =6 with
P/F factor.
Then, find the annual worth of the deposits with A/P factor.
At time t =8:
Because fi, P =$2400 [1 – (P/F, 5%, 11)(F/P, 2%,11)]/ [(5%) – (2%)]
=$21,841.98
At time t =6:
P =$21,841.98 (P/F, 5%, 2)
=$19,810.68
A =$19,810.68 (A/P, 5%, 8)
=$3064.71
7
22)
$52,000 was deposited in a savings account 7 years ago, and the account earned interest at
the rate of 12% per year. What is the amount of equal annual withdrawals that can be
made to completely deplete the fund 7 years from now if the first withdrawal will be made
now?
22)
Answer:
$20,660.95
Explanation:
Find the future worth of the deposit at year t = – 1. This will become the present
value of the uniform withdrawals that run from year 0 to year 7.
At t = – 1:
F =$52,000 (F/P, 12%, 6)
=$102,637.60
A =$102,637.60 (A/P, 12%, 8)
=$20,660.95
23)
Drugs, Inc. recently received approval from the Food and Drug Administration for its new
supplemental drug application for a 300–milligram tablet of an antiplatelet treatment. The
company invested $170 million in the research and development fund for this drug
application 7 years ago. What is the present worth of the investment now, if the company
achieves a rate of return of 2% per year?
23)
Answer:
$195,279,000.00
Explanation:
This is actually a future worth problem.
F =$170,000,000 (F/P, 2%, 7)
=$195,279,000.00
24)
What value of G makes the two series of cash flows described below equivalent at an
interest rate of 18% per year?
A: 14 annual deposits in the amount of $150
B: 7 annual deposits in the amount of $150 in the first year, and increasing by $G each year.
24)
Answer:
$20.02
Explanation:
Equate the present worth of both cash flows and solve for G.
Present worth of A =$150(P/A, 18%, 14)
=$150 (5.0081)
=$751.22
Present worth of B =$150 (P/A, 18%, 7) + G (P/G, 18%, 7)
=$150 (3.8115) + G (8.9670)
=$571.73 + G (8.9670)
Thus, G = [$751.22 –$571.73]/8.9670
=$20.02
8
25)
A major defense supplier expects to generate additional revenue from its recently won
government contract. The company expects the revenue will be $110 million in the first
year and the revenue increasing by $2.5 million each year for the next 4 years. What is the
future worth of the total revenue at the end of year 5, if the company’s rate of return is 18%
per year?
25)
Answer:
$816,904,746.00
Explanation:
Find the present worth of the revenue at time 0, and move to time 5 with the F/P
factor.
At t = 0:
P =$110,000,000 (P/A, 18%, 5) +$2,500,000 (P/G, 18%, 5)
=$357,070,000
At t =5:
F =$357,070,000 (F/P,18%, 5)
=$816,904,746.00
26)
What is the effective interest rate per 6 months for a nominal interest rate of 15% per year
compounded every 3 months?
26)
Answer:
0.0764 or 7.64%
Explanation:
Effective interest rate =(1 +r/M)M– 1 =(1+0.075/2)2–1
=0.0764 or 7.64%
27)
A U.S. auto maker plans to build two more plants in China as it aims to harness continued
growth in Asia. The company estimates that it must make annual investments of $40
million over a 8–year period. How much would the company have to invest now at an
interest rate of 3% per year to sufficiently provide for the annual payments, if the first
payment will begin 4 years from now?
27)
Answer:
$256,949,098.80
Explanation:
At time 3, P3=$40,000,000 (P/A, 3%, 8)
=$280,788,000.00
At time 0, P = P3 (P/F,3%, 3)
=$256,949,098.80
28)
Eight energy corporations made plans to increase their combined spending on efficiency
programs to $50 million per year for the next 8 years as a response to global warming
initiatives set by the government. What is the future worth of total investments at the end
of 8 years at an interest rate of 8% per year?
28)
Answer:
$531,830,000.00
Explanation:
F =$50,000,000 (F/A, 8%, 8)
=$531,830,000.00
29)
British Airways Plc plans to set aside investment funds now for replacing 34 of the airline’s
aging long–haul fleet of Boeing 747s and 767s, which will be delivered 5 years from now.
How much will the company need to have in its investment fund now if the cost of the
fleet is $1000 million and the company earns a rate of return of 3% per year?
29)
Answer:
$862,600,000.00
Explanation:
P =$1,000,000,000 (P/F, 3%, 5)
=$862,600,000.00
9
30)
Arian is about to borrow $2350 from his uncle. He has an option to repay the loan at the
end of year 5 with 10.75% simple interest per year or with 5% interest per year,
compounded annually.
What is the difference of the total interest paid over 5 years between the two options?
30)
Answer:
$613.86
Explanation:
Simple interest (I1) = Principal amount (P) x number of interest periods (N) x
interest rate per interest period (i)
P =$2350; N =5; i =10.75%
I1 =$1263.13
Compound interest total (I2) = Total amount due after 5 years – Principal
amount
Total amount due =P(I + i)N=$2999.26
I2 =$649.26
The difference of the total interest = I1 – I2 =$613.86
10
Answer Key
Testname: C4
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