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13 Jan 2020, 10:37
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Investment A: 2100
Investment B: 1616
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
55% (02:55) correct
45%
(03:05)
wrong
based on 279
sessions
History
Date
Time
Result
Not Attempted Yet
Jack divides $30,000 between two investments. He invests 35% of the money in Investment A, which pays 4% simple interest annually for 5 years. He invests the remainder of the money in Investment B, which pays 2% annual interest compounded semiannually for 4 years.
In the table below, identify the total interest earned, in dollars, for Investment A and the total interest earned, rounded to the nearest dollar, for Investment B that are consistent with the investments described above. Make only one selection in each column.
In the table below, identify the total interest earned, in dollars, for Investment A and the total interest earned, rounded to the nearest dollar, for Investment B that are consistent with the investments described above. Make only one selection in each column.
| Investment A | Investment B | |
| 392 | ||
| 870 | ||
| 1560 | ||
| 1616 | ||
| 2100 | ||
| 3347 |
ShowHide Answer
Official Answer
Investment A: 2100
Investment B: 1616
15 Jan 2020, 02:47
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Official Explanation
For this question, note that there’s no common condition that needs to be satisfied. Rather, there are two independent calculations.
The solution to this question starts with calculating how Jack divides the $30,000 between the two investments. Start by calculating 35% of $30,000. Remember that you can just use the onscreen calculator: 30,000 × 0.35 = 10,500. So, $10,500 is invested in Investment A and the rest, or $19,500, is invested in Investment B.
Next, it’s time to calculate the interest earned on each investment. Investment A earns simple interest at a rate of 4% per year for 5 years. To find simple interest, you multiply the principal amount, $10,500, by the interest rate, 0.04, by the time period, 5 years. Here’s what the calculation looks like:
$10,500 × 0.04 × 5 = $2,100
The onscreen calculator makes doing the calculation an easy, one-step operation. Just make sure that you use the right numbers from the problem!
For Investment B, the interest is compounded semiannually. That means that every six months the interest is added to the principal so that interest can be earned on the combined amount. There are several ways to calculate compound interest. One of the easiest is to divide the yearly interest rate by the compounding period. For this problem, the investment pays 2% per year, but the interest is compounded twice per year.
So, that’s 1% every six months. In four years, there are 8 compounding periods. So, to find the account balance at the end of 4 years, you’d calculate the interest for the first six months by multiplying by 0.01. Then, you’d add that amount to the principal and repeat the calculation. Keep calculating until you’ve done all 8 compounding periods. Of course, since you are multiplying each time, there’s a shorter way. Here’s what the overall calculation looks like.
\($19,500 × (1.01)^8 = $21,115.71\)
Now, to find the interest just subtract $19,500 from the account balance. The interest earned is $1,616 rounded to the nearest dollar. Here’s what your answers should look like just before you click next to move onto the next question in the Integrated Reasoning section:
For this question, note that there’s no common condition that needs to be satisfied. Rather, there are two independent calculations.
The solution to this question starts with calculating how Jack divides the $30,000 between the two investments. Start by calculating 35% of $30,000. Remember that you can just use the onscreen calculator: 30,000 × 0.35 = 10,500. So, $10,500 is invested in Investment A and the rest, or $19,500, is invested in Investment B.
Next, it’s time to calculate the interest earned on each investment. Investment A earns simple interest at a rate of 4% per year for 5 years. To find simple interest, you multiply the principal amount, $10,500, by the interest rate, 0.04, by the time period, 5 years. Here’s what the calculation looks like:
$10,500 × 0.04 × 5 = $2,100
The onscreen calculator makes doing the calculation an easy, one-step operation. Just make sure that you use the right numbers from the problem!
For Investment B, the interest is compounded semiannually. That means that every six months the interest is added to the principal so that interest can be earned on the combined amount. There are several ways to calculate compound interest. One of the easiest is to divide the yearly interest rate by the compounding period. For this problem, the investment pays 2% per year, but the interest is compounded twice per year.
So, that’s 1% every six months. In four years, there are 8 compounding periods. So, to find the account balance at the end of 4 years, you’d calculate the interest for the first six months by multiplying by 0.01. Then, you’d add that amount to the principal and repeat the calculation. Keep calculating until you’ve done all 8 compounding periods. Of course, since you are multiplying each time, there’s a shorter way. Here’s what the overall calculation looks like.
\($19,500 × (1.01)^8 = $21,115.71\)
Now, to find the interest just subtract $19,500 from the account balance. The interest earned is $1,616 rounded to the nearest dollar. Here’s what your answers should look like just before you click next to move onto the next question in the Integrated Reasoning section:
| Investment A | Investment B | Values |
| 392 | ||
| 870 | ||
| 1560 | ||
| Tick | 1616 | |
| Tick | 2100 | |
| 3347 |
Hope it helps
General Discussion
13 Jan 2020, 12:59
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Interest earned in A = (10500*4*5)/100 = 2100,in which 10500 = 35% of 30000
Interest earned in B =19500(1+1/100)^8 -19500= 1616
Posted from my mobile device
Interest earned in B =19500(1+1/100)^8 -19500= 1616
Posted from my mobile device
