1. 1. You invest $1,000 in a certificate of deposit that matures after 10 years
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Question
1. 1. You invest $1,000 in a certificate of deposit that matures after 10 years and pays 5 percent interest, which is compounded annually until the certificate matures.
a. How much interest will you earn if the interest is left to accumulate?
b. How much interest will you earn if the interest is withdrawn each year?
c. Why are the answers to a and b different?
2.A self-employed person deposits $3,000 annually in a retirement account (called a Keogh account) that earns 8 percent.
a. How much will be in the account when the individual retires at the age of 65 if the savings program starts when the person is age 40?
b. How much additional money will be in the account if the saver defers retirement until age 70 and continues the contributions?
c. How much additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70?
3. 3. A 45-year-old woman decides to put funds into a retirement plan. She can save $2,000 a year and earn 9 percent on this savings. How much will she have accumulated if she retires at age 65? At retirement how much can she withdraw each year for 20 years from the accumulated savings if the savings continue to earn 9 percent?
5. If a parent wants to have $100,000 to send a newborn child to college, how much must be invested annually for 18 years if the funds earn 9 percent? (Any current student who subsequently becomes a parent and wants to send a child to college should make this calculation early in the child
Explanation / Answer
1. a) The interest amount that the saver will earn if the interest is left to accumulate is calculated using the excel sheet:
Step1: Go to excel and click "insert" to insert the function.
Step2: Select the "FV" function to find out the interest amount that is accumulated.
Step3: Enter the values as Rate = 5%; Nper = 10; PMT = 0; PV = 1000
Step4: Click "OK" to get the desired value.
The value comes to "$1,628.89"
The future value at the time of maturity is $1,628.89
But the interest amount that is earned on the investment is calculated by deducting the invested amount from the future value.
Interest amount accumulated = Future value - Invested amount
= $1,628.89 - $1,000
= $628.89
This is the compounded interest amount or the accumulated amount on the investment.
b) The interest amount that the saver can withdraw each year is calculated using excel sheet:
Step1: Go to excel and click "insert" to insert the function.
Step2: Select the "PMT" function to find out the interest amount that can be withdrawn.
Step3: Enter the values as Rate = 5%; Nper = 10; PV = 1000; FV = 0
Step4: Click "OK" to get the desired value.
The value comes to "$129.5"
Therefore, the interest amount that can be withdrawn each year by the saver is $129.5
c) In the first part the interest is compounded year after year whereas in the second part, the interest amount is withdrawn in that particular year.
Since the interest is compounded year-after-year without making any withdrawl, the interest earned at the time of maturity is more than the interest that is withdrawn each year.
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