Kevin invested $8,000 for one year at a simple annual interest rate of

You can avoid calculation of compounded interest here.

$8,000 for one year at a simple annual interest rate of 6 percent = 6/100*8,000 = $480.

IF $10,000 were invested for one year at a simple annual interest rate of 8 percent, then it would earn 8/100*10,000 = $800. Since the interest is compounded semiannually, then it would earn interest on interest and actual interest would be higher.

So, the answer should be slightly more than $480 + $800 = $1,280. Only E fits.

Answer: E.
_________________

Simple interest earned on $8000 with rate of interest 6% for 1 year.

\(SI = \frac{8000 * 6 * 1}{100} = $480\)

Amount earned on $10,000 with rate of interest 8% for 1 year compounded semi annually.

Amount \(= \frac{104}{100} * \frac{104}{100} * 10,000 = $10816\)

CI = Amount - Principal

CI \(= 10,816 - 10,000 = $816\)

Total amount of interest earned \(=480 + 816 = $1296\). Answer E...

_________________
Please Press "+1 Kudos" to appreciate.

From the first investment, she would have earned 480$ at 6% interest on a total amount of 8000$

From the second investment, the interest is calculated at half yearly basis
The annual interest is 8%, so half-yearly interest is 4%

For the investment of 10000$, the interest for the first half of the year is 400$.

Since this interest is compounded, the interest of the
second half of the year is calculated for the principal of 10400$
Again the interest percentage is 4%, hence the interest for this half year is 4% of 10400 = 104*4 = 416$

Therefore, total interest from both investments is 480 + 400 + 416 = 1296(Option E)

We’ll use the simple interest formula for both parts of this question: I = P x r x t , where I = interest, P = principal, r = the annual interest rate, and t = the number of years (or part of a year) for which interest is earned.

Let’s first determine what Kevin earned from the $8,000 at 6 percent simple interest for 1 year:

8000 x 0.06 x 1 = $480

Next let’s determine what Kevin earned from the $10,000 for one year at an annual interest rate of 8 percent compounded semiannually. Note that semiannual compounding means that interest is computed twice a year, so for the first half of the year, we use t = 1/2:

10,000 x 0.08 x 1/2 = 10,000 x 0.08 x 1/2 = $400 = interest for the first half of the year.

Thus, the new principal is 10,000 + 400 = $10,400. This new principal earns interest for the second half of the year:

10,400 x 0.08 x 1/2 = $416

So, the total interest earned on the $10,000 was 400 + 416 = 816.

From the two investments, therefore, Kevin earned 480 + 816 = $1,296 in interest.

Answer: E
_________________

Hi All,

We're told that Kevin made two investments:
1) $8,000 for one year at a simple annual interest rate of 6 percent
2) $10,000 for one year at an annual interest rate of 8 percent compounded semiannually.

We're asked for the total amount of interest that Kevin earned on the two investments. This question requires that we use the two interest formulas:
Simple Interest = Principal x (1+rt)
Compound Interest = Principal x (1+r)^t
Where r and t are the interest rate/year and the amount of time (in years).

The first investment = $8,000(1.06) = $8,480 --> $480 in interest

The second investment calculates the interest SEMI-ANNUALLY, so we have to double the value of t, but halve the value of r....
The second investment = $10,000(1.04)^2

While that calculation might look a bit 'complex', we don't actually have to complete it. The first interest payment would equal $400 (since that is 4% of $10,000), but the second payment would be slightly HIGHER (since we'd be taking 4% of $10,400).

Thus, the TOTAL interest would equal $480 + $400 + (a little more than $400) = More than $1280. There's only one answer that matches...

Final Answer:

GMAT assassins aren't born, they're made,
Rich

(\(\frac{6}{100}\))(8,000) = (6)(80) = $480

(\(\frac{4}{100}\))(10,000) = (4)(400) = $400

(In the second half of the year the principal will be $10,000 + $400 = $10,400)

(\(\frac{4}{100}\))(10,400) = (4)(104) = $416

480 + 400 + 416 = 480 + 816 = $1,296

Answer E.

SI = p*r*t/100
= 8000*.06*1 = 480
CI= P ( 1+r/100) ^t
semiannually = 10000(1+.04)^2 = 10816; interest 816
total interest earned = 480+816 = 1296
IMO E

8000 x 0.06 x 1 = $480
10,000 x 0.08 x 1/2 = 10,000 x 0.08 x 1/2 = 400 = interest for the first half of the year.
Now principal is 10,000 + 400 = 10,400.
10,400 x 0.08 x 1/2 = $416 = interest for the second half of the year.
Total interest for one year = 400 + 416 = 816.
Total interest from both investment = 480 + 816 = 1,296

Ans E

E.

Case I: $8,000 for one year at a simple annual interest rate of 6 percent

SI = PRT/100 = 8000 *1 *6/100 = 480

Case II: $10,000 invested for one year at an annual interest rate of 8 percent compounded semiannually
Since compounded semi-annually: r = 8/2 = 4% ; time = 2

CI = P(1+r/100)^t - P = 10,000(1+4/100)^2 - 10000 = 816

Total interest = 480 + 816 = 1296
_________________

8000$ SI for 1 year @6% will be 6X(10%of 800)=6X80=480$
10000$ CI for 1 year @8% compounded semiannually will be successive percentage of 10000$ @4%
i.e 4+4+(4X4)/100=8.16%.
8.16% of 10000$=816$
Total CI+SI=1296$.

Interest for $8,000 in simple interest @6 \(=8000*\frac{6}{100}=480\) [For the whole year]

Interest for $10,000 in compound interest@8 \(=10000*\frac{4}{100}=400\) [For first six months]

Interest for $10,000 in compound interest@8 \(=(10,000+400)=10400*\frac{4}{100}=416\) [For next six months]

Total Interest for $10,000 in compound interest@8\(=400+416=816\)

Total interest Kevin earned \(=480+816=$1,296\)

The answer is \(E\)

Answer: Option E

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

8000 x 0.06 x 1 = $480
10,000 x 0.08 x 1/2 = 10,000 x 0.08 x 1/2 = 400 = interest for the first half of the year.
Now principal is 10,000 + 400 = 10,400.
10,400 x 0.08 x 1/2 = $416 = interest for the second half of the year.
Total interest for one year = 400 + 416 = 816.
Total interest from both investment = 480 + 816 = 1,296

Ans E

To calculate the interest earned on each investment, we can use the formula:

Simple Interest = Principal * Rate * Time

For the first investment:
Principal = $8,000
Rate = 6% = 0.06
Time = 1 year

Simple Interest for the first investment = $8,000 * 0.06 * 1 = $480

For the second investment:
Principal = $10,000
Rate = 8% = 0.08
Time = 1 year

Since the interest is compounded semiannually, we need to calculate the interest for each period separately.

First half-year interest:
Interest for the first half-year = Principal * (Rate/2) = $10,000 * (0.08/2) = $400

Second half-year interest:
Interest for the second half-year = (Principal + First half-year interest) * (Rate/2) = ($10,000 + $400) * (0.08/2) = $10,400 * 0.04 = $416

Total interest for the second investment = First half-year interest + Second half-year interest = $400 + $416 = $816

Now, we can calculate the total interest earned by adding the interest from both investments:

Total Interest = Simple Interest + Total interest for the second investment = $480 + $816 = $1,296

Therefore, the total amount of interest that Kevin earned on the two investments is $1,296, which corresponds to option (E).

what if the 8 percent compound interest were compounded semi annually for 3 years instead of just one?

does that mean we would take the $816 (the amount you get when you compound $10,000 at 8% interest rate semi annually) and multiply it by 3?

Hi sa800,

Compound Interest = Principal x (1+r)^t
Where r and t are the interest rate/year and the amount of time (in years). However, we have to adjust that formula IF we are calculating interest more often than just once a year.

If a $10,000 investment at 8% interest was calculated SEMI-ANNUALLY for 3 YEARS, we have to double the value of t (from 3 to 6), but halve the value of r (from 8 to 4)....

$10,000(1.04)^6

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com