Mitch and Bill are both ago 75. When Mitch was 24 years old, he began depositing
ID: 3121087 • Letter: M
Question
Mitch and Bill are both ago 75. When Mitch was 24 years old, he began depositing $1000 per year Into a savings account. He made deposits for the first 10 years, at which point he was forced to stop making deposits However, he left the money in the account, where H continued to earn interest for the next 41 years Bill Write start saving until he was 46 years old. but for the next 29 years he made annual deposits of $1000. Assume that both accounts earned an average annual return of 7% (compounded once a year). Complete parts (a) through (d) below. a. How much money does Mitch have in his account at age 75? At age 75. Mitch has $ in his account. (Round to the nearest cent as needed.) b. How much money does Bill have in his account at age 75? At age 75, Bill has $ in his account. (Round to the nearest cent as needed.) c. Compare the amounts of money that Mitch and Bill deposit into their accounts. Mitch deposits $: in his account and Bill deposits $ in his account. d. Draw a conclusion about this parable Choose the correct answer below. A. Both Bill and Mitch end with the same amount of money in their accounts, but Mitch had to deposit less money using his method. It is better to start saving as early as possible B. Bill ends up with more money in his account than Mitch because he make more deposits than Mitch, and each additional deposit will accrue merest each year C. Both Bill and Mitch have the same return on their investments despite using Afferent methods of saving. D. Mitch ends up with more money In his account despite not having deposited as much money as Bill because the interest that is initially accumulated accrues interest throughout the life of the account.Explanation / Answer
Mitch deposited $1000 at the compounding interest rate of 7% for 10 years.
lets calcualate the future value of these deposits at the end of 10 years.
FV = C * [((1+i)^n - 1)/i]
where C = Cash flow per period
i = interest rate
n = number of payments
FV = 1000 * [((1+0.07)^10 - 1)/0.07]
FV = 13816.45
Now, this amount remained deposited in the bank for next 41 years compounding at the rate of 7% per year
Amount = P*(1+r)^n
A = 13816.45 * (1+0.07)^41
A = 221376.42
Mitch deposisted, 1000*10 = $10000 overall in the bank account
In case of Bill, he started his saving at the age of 46 and deposited $1000 to bank account at the compounding interest rate of 7% for 29 years
hence at the age of 75 i.e. after 29 years, he has
FV = C * [((1+i)^n - 1)/i]
where C = Cash flow per period
i = interest rate
n = number of payments
FV = 1000 * [((1+0.07)^29 - 1)/0.07]
FV = 87346.53
Bill deposited, 1000*29 = 29000 overall in the bank account
(a) At the age of 75 Mitch has $221376.42 in his account.
(b)
At age 75, Bill has $87346.53 in his account.
(c)
Mitch deposits $10000 in his account and Bill deposits 29000 in his account.
(d) --> Option D