Mitch and Bill are both age 75. When Mitch was 23 years old, he began depositing
ID: 3143058 • Letter: M
Question
Mitch and Bill are both age 75. When Mitch was 23 years old, he began depositing 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 his money in the account, where it continued to earn interest for the next 42 years. Bill didn't start saving until he was 45 years old, but for the next 30 years he made annual deposits of $1400. Assume that both accounts earned an average annual return of 4% (compounded once a year). Complete parts (a) through (d) below.
At age 75, Mitch has how much money?
At age 75, Bill has how much money?
How much did they each deposit?
Explanation / Answer
Mitch
A = P (1 + r)^n -1)/r
here P = 1000 (I assumed as you did not give the data) , r = 0.04 , n = 10
hence
A = 1000 *(1.04^10 -1)/0.04 = 12006.1071
next 40 years
A = 12006.1071* (1 +0.04)^40
= 57641.5678
hence Mitch will have 57641.5678 at age of 75
b)
A = 1400 * (1.04^30 - 1)/0.04
= 78518.91285
c) Mitch deposited 1000*10 = 10,000
Bill deposited 1400*30 = 42,000
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