132 MORE INTERESTFORMULAS4-17 Find the value ofP for the following cash flow
diagram.
30001250rTT
p=?4-18 The following cash flow transactions are said to be
equivalent in terms of economic desirability at an in-
terest rate of 12% compounded annually. Determine
the unknown valueA.750
600TTI
A A A A 150
+ + + + +
0-1-2-3-4 =0-1-2-3-4-5
Cash Flow 1 Cash Flow 24-19 Upon the birth of his first child, Dick Jones decided to
.establish a savings account to partly pay for his son's
education. He plans to deposit $20 per month in the
account, beginning when the boy is 13 months old.
The savings and loan association has a current inter-
est policy of 6% per annum, compounded monthly,
paid quarterly. Assuming no change in the interest
rate, how much will be in the savings account when
Dick's son becomes 16 years old?
4-20 Mary Lavor plans to save money at her bank for use
in December. She will deposit $30 a month, begin-
ning on March 1 and continuing through November 1.
She will withdraw all the money on December 1. If
the bank pays 1/2% interest each month, how much
money will she receive on December 1?
-----..4-21 Derive an equation to find the end of year future sum
Fthat is equivalent to a series ofnbeginning-of-year
payments Bat interest ratei.Then use the equation
to determine the future sumF equivalent to sixB
payments of $100 at 8% interest.(Answer: F=$792.28)
4-22 If $200 is deposited in a savings account at the
beginning of each of 15 years, and the account draws
interest at 7% per year, how much will be in the ac-
count at the end of 15 years?
4-23 A company deposits $2000 in a bank at the end of
every year for 10 years. The company makes no de-
posits during the subsequent 5 years. If ~e bank pays
8% interest, how much would be in the account at end
of 15 years?
4-24 How much must be deposited now at 5.25%
interest to produce $300 at the end of ~very year for
10 years?
4-25 A student wants to have $30,000 at graduation 4 years
from now to buy a new car. His grandfather gave him
$10,000 as a high school graduation present. How
much must the student sa,\,e each year if he deposits
the $10,000 today and can earn 12% on both the
$10,000 and his earnings in a mutual fund his grand-
father recommends?
4-26 A city engineer knows that she will need $25 million
in 3 years to' replace toll booths on a toll road in the
city. Traffic on the road is estimated to be 20 million
vehicles per year. How much per vehicle should the
toll be to cover the cost of the toll booth replacement
project? Interest is 10%. (Simplify your analysis by
assuming that the toll receipts are received at the end
of each year in a lump sum.)
4-27 Using linear interpolation, determine the value of
(P/A,61/2%,10)from the compoundinteresttables.
Compute this same value using the equation. Why do
the values differ?
4-28 A man wants to help provide a college education for
his young daughter. He can afford to invest $600/yr
for the next 4 years, beginning on the girl's fourth
birthday. He wishes to give his daughter $4000 on
her 18th, 19th, 20th, and 2Pt birthdays, for a total
of $16,000. Assuming 5% interest, \yhat uniform
annual investment will he have to make on the girl's
8th through 17th birthdays? (Answer: $792.73)
4-29 How many months will it take to payoff a $525
debt, with monthly payments of $15 at the end of