Math 1140 - Fourrier - Nicolas Fourrier

Oct 13, 2011 - Give the present value formula for an annuity, then derive from it the expression for the number of payments in an annuity. (Detail your answer) ...
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MATH 1140 - Section 001

Fall 2011

Quiz 07 Name:

October 13, 2011

Directions: Write legibly, the use of documents is forbidden, giving or receiving aid on this assignement is forbidden. You will get zero if any of these happen.

1. Give the present value formula for an annuity, then derive from it the expression for the number of payments in an annuity. (Detail your answer) 3 points

−n

] Answer An = R[1−(1+i) ⇒ (1 + i)−n = 1 − AnR×i i Then apply the ln function of the absolute value of both sides (ln(x) is only defined for x > 0). ln|1− AnR×i | . n = ln(1+i)

2. Preston is looking at a new motorcycle that sells for $12, 500 and decides to save the money rather than going into debt to buy it now. His goal is to have all the money in hand within 3 years. His savings account is paying 4%(12). Find the monthly deposit. 3 points

n

Answer Sn = R (1+i) i)

−1

12,500× 0.04

R = (1+ 0.04 )3612−1 = $327.39 12 The monthly deposit is $327.39.

3. On Sarah’s 10th birthday, her mother deposited $100 into a savings account earning 7%. Her mother continued such $100 deposits, making the last one on Sarah’s 23rd birthday. At that time Mom withdrew it all for a wedding gift for Sarah. How large was the gift ? 4 points

Answer Note that there are 13 years between the first and last deposit, thus by the Fence Post Principle, there are 14 years. 14 −1 = 2255.05 Sn = 100 (1+0.07) 0.07 The gift is $2255.05.