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# Calculating Present and Future Value and Loan Amortizations

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Complete problems 2, 4, 13, 17, 26, 30, 37, 38, & 40 on text pp. 207-211 of Ch. 6.

2. If you require a 9 percent return on your investments, which would you prefer?
a. \$5,000 today
b. \$15,000 five years from today
c. \$1,000 per year for 15 years

4. The Mutual Assurance and Life Company is offering an insurance policy
under either of the following two terms:
a. Make a series of 12 payments of \$1,200 at the beginning of each of the
next 12 years (the first payment being made today)
b. Make a single lump-sum payment today of \$10,000 and receive coverage
for the next 12 years
If you had investment opportunities offering an 8 percent annual return,
which alternative would you prefer?

13. You decide to purchase a building for \$30,000 by paying \$5,000 down and assuming
a mortgage of \$25,000. The bank offers you a 15-year mortgage requiring
annual end-of-year payments of \$3,188 each. The bank also requires you to
pay a 3 percent loan origination fee, which will reduce the effective amount the
bank lends to you. Compute the annual percentage rate of interest on this loan.

17. Construct a loan amortization schedule for a 3-year, 11 percent loan of
\$30,000. The loan requires three equal, end-of-year payments.

26. IRA Investments develops retirement programs for individuals. You are 30
years old and plan to retire on your 60th birthday. You want to establish a plan
with IRA that will require a series of equal, annual, end-of-year deposits into
the retirement account. The first deposit will be made 1 year from today on
your 31st birthday. The final payment on the account will be made on your
60th birthday. The retirement plan will allow you to withdraw \$120,000 per
year for 15 years, with the first withdrawal on your 61st birthday. Also at the
end of the 15th year, you wish to withdraw an additional \$250,000. The retirement
account promises to earn 12 percent annually.
What periodic payment must be made into the account to achieve your
retirement objective?

30. Crab State Bank has offered you a \$1,000,000 5-year loan at an interest rate of
11.25 percent, requiring equal annual end-of-year payments that include both
principal and interest on the unpaid balance. Develop an amortization schedule
for this loan.

37. Using an online mortgage financial calculator (see http://moyer.swlearning.com),
solve for the monthly savings and the number of months it takes to recoup the
refinancing costs in problem 34. (Hint: Under the question "What will it cost
you?" enter 2850 for "Other" and 0 for all other items.)

38. Use an online savings or retirement calculator (see http://moyer.swlearning.
com) to solve following problem: You are now 30 years old and would like to
accumulate \$2,000,000 in your retirement account at age 65. You currently
have \$50,000 saved in the retirement account. How much must you set aside at
the end of each year over the next 35 years to attain your retirement goal if
the account earns 6.5 percent per year? How much would you have to set aside
each year if you currently have a zero balance in the retirement account?

40. Using one of the mortgage loan calculators available on the Internet (see
http://moyer.swlearning.com), do a loan amortization for a \$150,000, 30-year
mortgage loan at a rate of 5 percent and answer the following questions:
a. How much is the monthly payment?
b. How much of the first payment (i.e., year 1, month 1) goes towards interest?
How much toward principal reduction?
c. How much of the 180th payment (i.e., year 15, month 12) goes toward
interest? How much toward principal reduction?
d. What is the remaining balance on the loan at the end of the fifth year?

#### Solution Preview

Complete problems 2, 4, 13, 17, 26, 30, 37, 38, & 40 on text pp. 207-211 of Ch. 6.

2. If you require a 9 percent return on your investments, which would you prefer?
a. \$5,000 today

b. \$15,000 five years from today

PV = FV/ (1+R)N where PV is the present value
FV is the future value
R is the interest rate
N is the period
PV = 15,000/(1 + 0.09)5
= 9,748.97

c. \$1,000 per year for 15 years

PVA = W x 1 - 1 where PVA is the present value
(1 + R)N W is the amount required of annuity each year
R R is the interest rate
N is the period

PVA = 1,000 x 1 - 1
(1 + 0.09)15
0.09

PVA = 8,060.69

Answer: I would prefer choice b. because it provides highest present value.

4. The Mutual Assurance and Life Company is offering an insurance policy under either of the following two terms:

a. Make a series of 12 payments of \$1,200 at the beginning of each of the next 12 years (the first payment being made today)

You have to use annuity due to find the fair value.

PVA = W x 1 - 1 x (1 + i) where PVA is the present value
(1 + i)n W is the amount required to pay yearly
i i is the interest rate
n is the period

PVA = 1,200 x 1 - 1 x (1 + 0.08)
(1 + 0.08)12
0.08

PVA = 9,766.76

b. Make a single lump-sum payment today of \$10,000 and receive coverage for the next 12 years

If you had investment opportunities offering an 8 percent annual return, which alternative would you prefer?

I would prefer alternative a. because the present value is lower.

13. You decide to purchase a building for \$30,000 by paying \$5,000 down and assuming
a mortgage of \$25,000. The bank offers you a 15-year mortgage requiring annual end-of-year payments of \$3,188 each. The bank also requires you to pay a 3 percent loan origination fee, which will reduce the effective amount the bank lends to you. Compute the annual percentage rate of interest on this loan.

Actual amount to be lent = \$25,000 - (\$25,000 x 3%) = \$24,250

PVA = W x 1 - 1 where PVA is the present value
(1 + R)N W is the amount required of annuity each year
R R is the interest rate
N is the period

\$24,250= 3,188 x 1 - 1
...

#### Solution Summary

This solution is comprised of a detailed explanation to calculate present and future value and loan amortizations and construct a loan amortization schedule for a 3-year, 11 percent loan of \$30,000.

\$2.49