Jack invests $500 at a certain annual interest rate, and he invests another $1000 at an annual rate that is one-half percent higher. If he receives a total of $65 interest in 1 year, at what rate is the $500 invested?
Jack invests $500 at a certain annual interest rate, and he invests another $1000 at an annual rate that is one-half percent higher. If he receives a total of $65 interest in 1 year, at what rate is the $500 invested?L
Let the $500 be invested @ x,
$1,000 will be invested x + 0.5, but we have:
500*x/100 + 1,000*(x/100 + 0.005) = 65, solve for x
Solve for x:
1000 (x/100 + 0.005) + 5 x = 65
Put each term in x/100 + 0.005 over the common denominator 100: x/100 + 0.005 = x/100 + 0.5/100:
1000 x/100 + 0.5/100 + 5 x = 65
x/100 + 0.5/100 = (x + 0.5)/100:
1000 (x + 0.5)/100 + 5 x = 65
1000/100 = (100×10)/100 = 10:
10 (x + 0.5) + 5 x = 65
10 (x + 0.5) = 10 x + 5.:
10 x + 5. + 5 x = 65
Grouping like terms, 10 x + 5 x + 5. = (10 x + 5 x) + 5.:
(10 x + 5 x) + 5. = 65
10 x + 5 x = 15 x:
15 x + 5. = 65
Subtract 5. from both sides:
15 x + (5. - 5.) = 65 - 5.
5. - 5. = 0:
15 x = 65 - 5.
65 - 5. = 60.:
15 x = 60.
Divide both sides of 15 x = 60. by 15:
(15 x)/15 = 60./15
15/15 = 1:
x = 60./15
60./15 = 4.:
Answer: | x = 4%
+118609
Jack invests $500 at a certain annual interest rate, and he invests another $1000 at an annual rate that is one-half percent higher. If he receives a total of $65 interest in 1 year, at what rate is the $500 invested?
Here is a start :)
I am using I=PRT which is the same for both simple and compound interest if the time unit is just one. i.e. t=1
Solve this and you will get the initial rate as a decimal. Multiply it by 100 to get the percentage.
\(65 = 500*r+1000(r+0.005)\)
