Manuel Rios wishes to determine how long it will take an initial deposit of $10,
ID: 2741708 • Letter: M
Question
Manuel Rios wishes to determine how long it will take an initial deposit of $10, 000 to double. a. If Manuel earns 10% annual interest on the deposit, how long will it take for him to double his money? b. How long will it take if he earns only 7% annual interest? c. How long will it take if he can earn 12% annual interest? d. Reviewing your findings in parts a, b, and c, indicate what relationship exists between the interest rate and the amount of time it will take Manuel to double his money. e. Manuel assumes that the money will be doubled in five years. Explain why the rate of return is NOT 20 percent per year. Anna Waldheim was seriously injured in an industrial accident. She sued the responsible parties and was awarded a judgement of $2, 000, 000. Today, she and her attorney are attending a settlement conference with the defendants. The defendants have made an initial offer of $156, 000 per year for 25 years. Anna plans to counter offer at $255, 000 per year for 25 years. Both the offer and the counter offer have a present value of $2, 000, 000, the amount of the judgement. Both assume payments at the end of each year. a. What interest rate assumption have the defendants used in their offer (rounded to the nearest whole percent)? b. What interest rate assumption that Anna and her lawyer used in their counter-offer (rounded to the nearest whole percent)? c. Anna is willing to settle for an annuity that carries an interest rate assumption of 9%. What annual payment would be acceptable to her? Make a proposal letter addressed to the defendants.Explanation / Answer
Answer for question no.a:
Initial deposit=$10,000.
Interest earned=10% per annum.
The target amount is $20,000.
Formula to be used for this compound interest formula A=P(1+r/100)^n
Here A= Maturity amount=$20,000.
P is the prinicipal amount=$10,000
r= rate of interest =10%=.10
n=number of periods.
$20,000 =$10,000(1+.10)^n.
Approximate period for doubling can be obtained by using rule of 72, which means by dividing 72 with the interest rate.
=72/10=7.2
Subtituting this value for n in the formula
A=$10,000*(1.1)7.2
A=$19,862.
Substituting 7.3 for n A=$20,052.41.
Therefore, approximately it would take 7 years and 12*.3 =3.6 months for the amount to double.
Answer for question no.b:
If the annual interest rate=7%, then the amount would double in is obtained by following the same procedure as mentioned above.
Using thumb rule of 72
=72/7
=10.285
Substituting this for n in the compound interest formula =10000*(1+.07)^10.285
=20055.48.
Therefore, the amount would get doubled in 10 years and 0.285 *12 =3.42 months.
Answer for question no.c:
Interest rate per annum=12%.
Using thumb rule of 72, n=72/12 = 6 years.
Now, substituting the values in the compound interest formula =10,000*(1.12)^6
=19,738.22.
At the end of 6 years the balance is $19,738.22, but the amont is to be doubled so, the short fall is $20,000 -$19,738.22
=$261.78.
The amount of per day interest earned is $19,738.22 *12%/365=6.489.
Now dividing $261.78 by per day interest, the number of days the deposit must be there to earn $261.78 interest is obtained.
=$261.78/6.489
=40.340.
Therefore, the amount gets doubled in 6 years 40 days.
Answer for question no.d:
It is observed that the higher the interest rate, the lesser time it is taking to double the amount.
Answer for question no.e:
If the amount is getting doubled in 5 years, the interest rate is not 20% because the interest earned in year 1 becomes principal for the second year, hence the prinipal amount is not same for every year.
So, if the amount is to be double in 5 years, then the rate would be =14.88% this is obtained by using the compound intrest formula $20,000 =10000(1+x)^5
2^1/5 =1+x
x=1.148698 -1
x=.14869
therefore x=14.87% per annum.
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