QUESTION: 4-3

(4-3)

An annuity is defined as a series of payments of a fixed amount for a specific number of periods.  Thus, $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity.  However, the entire series does contain an annuity.  Is this statement true or false?

PROBLEMS: 4-1, 4-2, 4-12, 4-29

(4-1)  If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?

(4-2)  What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?

(4-12) 

Find the future value of the following annuities.  The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities.  (Notes: See the Hint to Problem 4-9.  Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

a.  $400 per year for 10 years at 10%

b.  $200 per year for 5 years at 5%

c.  $400 per year for 5 years at 0%

d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due

(4-29) Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $10,000 as part of the payment.  The mortgage has quoted (or nominal) interest rate of 10%; it calls for payments every 6 months, beginning on June 30, and is to be amortized over 10 years.  Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year.  (This interest will be income to your aunt and a deduction to the buyer of the house.)  To the closest dollar, what is the total amount of interest that was paid during the first year?

Aunt borrows $10000

Using the payment formula

a  =  (P(1 + r)Yr ) / ( (1 + r)Y - 1 )

  =  10000(1+0.05)20*.05 / ((1+.05)20 – 1)

  =  The loan amount to be paid at the end of six months comes out to be $802. 5

Now the interest paid

For the first six months the interest is $500 and the amount paid is  $802.5 and the excess 302.5 would be deducted from the sum, so the new sum for the next period is $9697.5. The interest of the new sum for the next six months is $484.875. So the net interest paid by aunt for one year is $984.88.