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

Question

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%

Explanations would be appreciated

A. 19%
B. 20%
C. 21%
D. 22%
E. 25%

pavanpaone · Accepted Answer

investment 1000 dollars
1 st year total gained = 100
total amount end of first year = 1100 
second year account increased by 10 % = 1100*0.1 = 110 
 therefore total amount by second year end = 1210

so total percentage increase in money = (1210-1000)*100/1000 = 21 %

unceldolan · Answer

%-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 · Answer

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

adkikani · Answer

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?

generis · Answer

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.

sanjeevsinha082 · Answer

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.

ManishaPrepMinds · Answer

Initial  = $1000
 Year 1 : $1,100
 Year 2 : $1,100 × 1.1 = $1,210
Final ratio = $1,210/$1,000 = 1.21
Ratio increase = (final ratio - 1) = 0.21 
 Percentage increase :
= 0.21*100 = 21%

Answer: 21%

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

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

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