Sam opened a money-market account that pays 2% simple interest. He started the account with $7,000 and made no further deposits. When he closed the account, he had earned $560 in interest. How long did he keep his account open?
Question 3
Terry invests $3,000, at 10% interest, compounded semiannually for 12 years. Use the compound interest formula to calculate the compound amount for his investment.
a.
$9,675.30
b.
$6,760.00
c.
$6,663.28
d.
$9,860.00
Well, it seems like Sam's money was pretty happy in that money-market account. Let's see how long the party went on!
If Sam earned $560 in interest with a 2% simple interest rate, we can use a bit of clown math to figure out how many years he kept the account open.
First, let's find out how much interest he earned each year. To do that, we can divide the total interest he earned ($560) by the interest rate (2%).
$560 / 2% = $28,000
Ah, now we see our clown friend Sam earned $28,000 in interest over the years. But that's not all the clown math has in store for us!
Since Sam started with $7,000, we need to find out how many times that amount fits into $28,000.
$28,000 / $7,000 = 4
Hurrah! It seems like our clown friend Sam kept his account open for 4 years. That's a great performance for a money-market account!
To determine how long Sam kept his account open, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Let's plug in the given values:
$560 = $7,000 * 0.02 * Time
We can now solve for Time:
Time = $560 / ($7,000 * 0.02)
Calculating it:
Time = $560 / ($140)
Time = 4 years
Therefore, Sam kept his account open for 4 years.
To determine how long Sam kept his money-market account open, we need to use the formula for simple interest:
Interest = Principal * Rate * Time
Let's break down the information given in the question:
Principal (initial deposit) = $7,000
Rate = 2% or 0.02 (since it's given as a percentage)
Interest = $560
We can rearrange the formula to calculate time:
Time = Interest / (Principal * Rate)
Plugging in the values, we get:
Time = $560 / ($7,000 * 0.02)
= $560 / $140
= 4
Therefore, Sam kept his account open for 4 units of time. Given that the rate is in percentage per year, we can conclude that each unit of time corresponds to one year. Hence, Sam kept his account open for 4 years.
7000*n*.02 = 560
n = 4 years
check:
2% interest per year is $140 x 4 = $560