adkikani wrote:

generis **Quote:**

Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued $100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of $1,000 ?

A. 19%

B. 20%

C. 21%

D. 22%

E. 25%

**Quote:**

Year 1 interest: $100

Year 2 interest, 10% of 1,100 = $110

Total interest = 100 + 110 = $210 (which equals the change in value)

\(\frac{change}{original}\) x 100 = percent change

\(\frac{210}{1000}\) = .21 x 100 = 21%

Answer C

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

Percent change using

multipliers= compound interest rate

•

Multipliers - TOTAL factor increaseMultiplier, 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.
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