Two years ago, Sam put $1,000 into a savings account.

%-change = change in value / original value

original value here: 1000 $

change value: we need to calculate the account after year 2. we take our 1100 $ after 1 year and calculate 10 % which is 110 $. we get 1210 $ after 2 years. hence there was a change in value of 210 $.

plug into formula : 210 $ / 1000 $ = 21 / 100 =21 %

Thus C.

Hope it helps.

generis






We are not given rate of interest (r) directly. Did you calculate the same by knowing principal amount (Rs.1000),
tenure (1 year), interest (Rs. 100) and using equation: Interest = PrT/100 for the first year and then using the same for the second year?

niks18
Is the highlighted part in question required to be given?

adkikani , I think you ask two questions.

1) did I use simple interest rate equation?
2) why does it look as if I did?

• No, I did not use interest rate
I used net change in money amount for each year

Year 1's change amount is given: + $100
Year 2's change rate is given:
10% increase on $1,100 = + $110

Then I calculated percent change from net amount change,
see original post. (Change/Original * 100)

Your question about the highlighted portion
is interesting.

If Sam left the earned interest in the bank;
and if Sam left the account alone;
of course we can calculate the amount in the account.
He put in $1000. He earned $100. His total = $1,100.

But we don't know what Sam did with the account.
The highlighted portion tells us that he left it alone.

• I suspect it appears that I used interest rates
because for any given first year,
if simple interest rate = annual compound interest rate,
amount yielded is identical.

• Use interest rate? Yes, but . . .
If I were to calculate percent increase
using interest rates, I would:

1) not use strict SI (it's inaccurate)*
2) use multipliers or
3) use compound annual interest

For #2 and #3, I would omit principal amount. Not needed.

Percent change using
multipliers= compound interest rate

• Multipliers - TOTAL factor increase

Multiplier, Year 1? Deduce from base + interest
\(1,000 + 100 = 1,100\)
Multiplier: \(\frac{1,100}{1,000}= 1.1\)

Multiplier for Year 2? Given.
10% increase on extant amount = \(1.1\)

Multipliers: TOTAL increase factor?
(Year 1 multiplier * Year 2 multiplier) = total increase factor
Total increase factor: \((1.1 * 1.1) = 1.21\)
Original base? \(1\)

• Compound annual interest: TOTAL factor increase

\(A_{final}=P(1+.10)^{nt}\)
\(A_{final}=P(1.1)^{1*2}\)
\(A_{final}=P(1.1)^2\)
\(A_{final}=1.21P\)

\(A_{original}= P\)

• Percent increase:

\(\frac{New-Old}{Old}*100\)

\((\frac{1.21-1}{1}*100)=(\frac{.21}{1}*100)\)
\(= .21*100=21\) percent

OR \((\frac{1.21P-1P}{1P}*100)=(\frac{.21P}{1P}*100)\)
\(=.21*100=21\) percent

Hope that answers your question.

*SI amount for both years?
INCORRECT if years are taken together
Run this formula for SI:
\(A_{final} = P(1 + rt)\)
Total after two years is $1,200. Not correct.

If you separate Year 1 and Year 2;
change \(P\) from $1,000 to $1,100;
and change \(t\) from 2 to 1;
SI formula will work.

Given an initial deposit of $1,000, we must figure out the ending balance to calculate
the total percent change.
After the first year, Sam's account has increased by $100 to $1,100.
After the second year, Sam's account again increased by 10%, but we must take 10%
of $1,100, or $110. Thus the ending balance is $1,210 ($1,100 + $110).
To calculate the percent change, we first calculate the difference between the ending
balance and the initial balance: $1,210 – $1,000 = $210. We divide this difference by
the initial balance of $1,000 and we get $210/$1,000 = .21 = 21%.
The correct answer is C.

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