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# Calculating Present and Future Value and Loan Amortizations

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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 due 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 three 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 1st withdraw on your 61st birthday. Also, at the end of your 15th year, you wish to withdraw an additional \$250,000. The retirement plan promises to earn 12 percent annually.
What periodic payment must be made into the account to achieve your retirement objectives?

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.

38.
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.
Do a loan amortization for a \$150,000, 30 year mortgage loan at a rate of 5% and answer the following questions:
a. How much is the monthly payment?
b. How much of the 1st payment is goes toward interest? How much toward principal reduction?
c. How much of the 180th payment (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

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

First, you have to find the present value for three alternatives.

a. present value will be \$5,000

b. 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
PV = 9,748.97

c. 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

We will prefer b. because the present value is the highest.

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 due 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?

Find the present value for first term.

PVA = 1,200 x 1 - 1 + 1,200
(1 + 0.08)11
0.08

PVA = 8,566.76 + 1,200 = 9,766.76

Choose the first term 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 ...

#### Solution Summary

This solution is comprised of a detailed explanation to calculate present and future value and loan amortizations for various finance problems.

\$2.49