1. Explain how multiplication by 1.07 represents growth by 7%. If you have $100 in an...

Explain how multiplication by 1.07 represents growth by 7%.
If you have $100 in an account that grows by 7% per year, how much money will you have after 1 year?
If you keep that money in the account, how much will you have after the second year?
Explain how 100 * (1.07)9 represents growth by 7% each year for nine years in a row.
Note that 7*9=63. What does 100 * (1.63) represent in terms of growing the number 100 by a percent?
Which of the two numbers below is bigger?
a. 100 * (1.07)9 b.100 * (1.63)
1. Fill in the blanks:
2. If we had instead considered growth by 2% each year for nine years and compared that to growth by 18% one year, what would have changed and what would have stayed the same in the questions above?
3. Growing a quantity by 7% nine times in a row will result in ___________ (less, more, the same amount of) growth __________ (than, as) growing by that quantity 63% just once.

Solutions

Expert Solution

1)
This problem is based on Compound interest is the addition of interest to the principal sum of a loan every year. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Future value = Present Value x (1 + growth rate)
After one year = Future value = $100 x (1 + 7%)	107
After Two year = Future value = $100 x (1 + 7%)^2	114.49
or
After Two year = Future value = $107 x (1 + 7%)	114.49
After 9 years = Future value = $107 x (1 + 7%)^9	$ 183.85
Its not 7*9=63. but .07^ 9 means (.07 x .07 x .07 x .07 x .07 x .07 x .07 x .07 x .07 )	1.838

Which of the two numbers below is bigger?
100 x (1.07)^9	$ 183.85	Greater
100 x (1.63)	$ 163.00

If we had instead considered growth by 2% each year for nine years and compared that to growth by 18% one year, what would have changed and what would have stayed the same in the questions above?
Growing a quantity by 7% nine times in a row will result in more growth than, growing by that quantity 63% just once.

ekkarill92 answered 1 year ago

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