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Answers
Sample Exam
Five |
Annuities
- You may
round your answers to whole dollars.
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| 1. |
(10 pts.)
Payments of $5,000 were made at the end of each quarter
into an account that pays 11% compounded quarterly. How
much was in the account after six years?
| Acc.
Value: Ordinary annuity |
P= 5000
n = 6 x 4 = 24
i =
 |
S
= 5000 S
S = 5000(33.36822199)
S = 166,841.11 or 166,841 |
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| 2. |
(20 pts.)
Payments of $750 at the end of month for 3 years at 9%
compounded monthly. Payments of $550 beginning of
month for 4 years at 6% compounded monthly.
Which has greater present value?
P = 750
n = 3 x 12 = 36
i =
A = 750(31.44680525)
A =
23,585.10 or 23,585
Greater Present Value |
P = 550
n = 4 x 12 = 48
= 550(41.79321937+1)
=
23,536.27 or 23,536
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| 3. |
(15 pts.)
Cindy used part of an insurance settlement to purchase an ordinary
annuity that would pay her $5,000 each six months for 10
years. How much did the annuity cost if the interest rate is
10% compounded semiannually?
Present Value: Ordinary Annuity
P = 5000
n = 10 x 2 = 20
A = 5000
A = 5000(12.46221034)
A = 62,311.05 or 62,311
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| 4. |
(15 pts.)
Find the interest earned on an annuity due if
payments of $2,000 per year are made for 15 years into an
account paying 5% compounded annually.
Interest (made) =
P = 2000
n = 15
i = 5%
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=
2000(23.65749177 - 1)
= 2000(22.65749177)
=
45,314.98 or 45,315
I(made)
= 45315-15(2000)
I(made) = 15,315
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| 5. |
(20 pts.)
For every dollar an employee deposits at the beginning of
each quarter into a company thrift plan paying 9% compounded
quarterly, a company deposits $0.75 into the employee's account.
An employee deposited $600 each quarter for four years.
Find the amount in the account after this time.
Accumulated
Value: annuity due
P = 600
+.75(600) = 1050
n = 4 x 4 = 16
= 1050(20.43301957
- 1)
= 1050(19.43301957)
= 20,404.67 or 20,405
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Alternate
(re: 75% from employee)
P = 600 (Employee)
=
600(19.43301957) = 11,660 (Employee)
Employer = .75(11,660) = 8745
11,660 Employee
8,745 Employer
20,405
Total |
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| 6. |
(20 pts.)
Debbie deposited $400 per month into an ordinary annuity
with an interest rate of 6% compounded monthly, while Lynn
deposited $1,100 per quarter into an annuity due with interest
rate of 7% compounded quarterly. After four years, who has the
greater amount on deposit and who made the most interest? |
|
Debbie |
Lynn |
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Accumulated Value:
Ordinary annuity
P = 400
n = 4 x 12 = 48
S = 400(54.09783222)
S = 21,639
I(made) = S -
nP = 21,639-48(400)
I(made) = 2439 |
Accumulated
Value; Annuity due
P = 1100
n = 4 x 4 = 16
 =
1100(19.60160656 - 1)
=
1100(18.60160656)
=
20,462I(made) =
- nP = 20,462 - 16(1100)
I(made = 2862
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Debbie
had greater amount on deposit.
Lynn made more interest.
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Copyright © Jim Pack,
2000. All Rights Reserved. Last modified
11/20/07
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