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Compound Interest Theory Chap 3 Solutions

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Submitted By pattymath816
Words 1204
Pages 5
Chapter 3

1. The equation of value using a comparison date at time [pic] is
[pic]
Thus,
[pic]

2. The down payment (D) plus the amount of the loan (L) must equal the total price paid for the automobile. The monthly rate of interest is [pic] and the amount of the loan (L) is the present value of the payments, i.e.
[pic]
Thus, the down payment needed will be
[pic]

3. The monthly interest rate on the first loan (L1) is [pic] and
[pic]
The monthly interest rate on the second loan (L2) is [pic] and
[pic]
The payment on the second loan (R) can be determined from
[pic]
giving
[pic]

4. A’s loan: [pic]
[pic]
so that the total interest would be
[pic]

B’s loan: The annual interest is
[pic]
so that the total interest would be
[pic]
Thus, the difference is
[pic]

5. Using formula (3.2), the present value is
[pic]
This expression then becomes
[pic]
6. We are given [pic] so that [pic] Also, we are given [pic] so that [pic] But [pic] so that [pic] This equation is the quadratic [pic] so that [pic] Then applying formula (1.15a), we have [pic]

7. We know that [pic] and directly applying formula (3.8), we have
[pic]

8. The semiannual interest rate is [pic] The present value of the payments is
[pic]

9. We will use a comparison date at the point where the interest rate changes. The equation of value at age 65 is
[pic]
so that
[pic]
to the nearest dollar.

10. (a) Using formulas (3.1) and (3.7)
[pic]

(b) Using formulas (3.3) and (3.9)
[pic]

(c) Each formula can be explained from the above derivations by putting the annuity-immediate payments on a time diagram and adjusting the beginning and end of the series of payments to turn each into an annuity-due.

11. We know that
[pic]
Thus, [pic] and [pic] so that [pic]

Finally,
[pic]

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