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Difficulty:
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Question Stats:
64% (02:50) correct
36%
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wrong
based on 266
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A merchant invested $10,000 at 5% annual interest, compounded semi-annually, and an amount of $X at 5% simple annual interest. At the end of the first year, the total interest earned on each investment was the same. What is the value of X?
a. $10,000
b. $10,125
c. $10,250
d. $10,500
e. $10,825
a. $10,000
b. $10,125
c. $10,250
d. $10,500
e. $10,825
25 Jan 2017, 03:56
Kudos
Bookmarks
Here we go,
I don't think that's a difficult question to someone who knows the formula to calculate Compound Interes and Simple Interest.
Compound Interest is calculated using -
A = P (1 + r/n)^(nt) --------------- (1)
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
and
Simple Interest is calculated using -
SI = (P x R x T)/100 --------------- (2)
Principal = P, Rate = R% per annum (p.a.) and Time = T years
Back to the question now.
A merchant invested $10,000 at 5% annual interest, compounded semi-annually
Using equation 1
10000 * (1 + 0.05/2)^2 = 10506.25
Total interest earned in this case = 10506.25 - 10000 = 506.25 ------- (a)
The question mentioned that tt the end of the first year, the total interest earned on each investment was the same..
Using equation (2)
506.25 = X * 0.05 * 1
so X = 10125
Option B should be the answer....
Now to answer to "im looking for a fast way to solve this."
I would have suggested to use the approximation technique by removing the decimal .25 in (a), but considering that the options are pretty close to each other, I don't think of any fast way to solve it as of now....
I don't think that's a difficult question to someone who knows the formula to calculate Compound Interes and Simple Interest.
Compound Interest is calculated using -
A = P (1 + r/n)^(nt) --------------- (1)
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
and
Simple Interest is calculated using -
SI = (P x R x T)/100 --------------- (2)
Principal = P, Rate = R% per annum (p.a.) and Time = T years
Back to the question now.
A merchant invested $10,000 at 5% annual interest, compounded semi-annually
Using equation 1
10000 * (1 + 0.05/2)^2 = 10506.25
Total interest earned in this case = 10506.25 - 10000 = 506.25 ------- (a)
The question mentioned that tt the end of the first year, the total interest earned on each investment was the same..
Using equation (2)
506.25 = X * 0.05 * 1
so X = 10125
Option B should be the answer....
Now to answer to "im looking for a fast way to solve this."
I would have suggested to use the approximation technique by removing the decimal .25 in (a), but considering that the options are pretty close to each other, I don't think of any fast way to solve it as of now....
25 Jan 2017, 10:03
Kudos
Bookmarks
magniv123
A merchant invested $10,000 at 5% annual interest, compounded semi-annually,
and an amount of $X at 5% simple annual interest. At the end of the first year, the
total interest earned on each investment was the same. What is the value of X?
a. $10,000
b. $10,125
c. $10,250
d. $10,500
e. $10,825
im looking for a fast way to solve this.
thank you:)
and an amount of $X at 5% simple annual interest. At the end of the first year, the
total interest earned on each investment was the same. What is the value of X?
a. $10,000
b. $10,125
c. $10,250
d. $10,500
e. $10,825
im looking for a fast way to solve this.
thank you:)
Hi,
I can think of 2 ways..
1) substitution..
Start from the middle value so that you can eliminate 2 choices either one on top or below..
Equation is \(10000(1+\frac{2.5}{100})^2-10000=\frac{10250*5}{100}\)
10000*1.025*1.025-10000~500..
But 10250*.05~ 612..
So it has to be less than 10250.. AND ofcourse it has to be more than 10000
Only value left is 10125..
2) method..
Leave 10000 and take it as 1..
So \((1+\frac{2.5}{100})^2-1=\frac{x*5}{100}\)
1.025*1.025-1=x/20.......0.00506=x/20.....X=0.506*20=1.012..
Ans= 1.012*10000=10120
B
