In 6 years, Jim wants to have $47,230 to buy a new car.
(a) How much must Jim save each month if the interest rate is 6% compounded monthly?
$ ______
(b) How much of the $47,230 does Jim actually deposit and how much of it is interest?
$______(deposit)
$______(interest)
http://www.google.com/search?rlz=1C1GGGE_enUS379US379&sourceid=chrome&ie=UTF-8&q=calculating+interest
One of these links should have a formula to help you calculate these.
To calculate the amount Jim must save each month, we can use the formula for calculating the future value of a series of equal monthly deposits. The formula is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Monthly deposit amount
r = Monthly interest rate (as a decimal)
n = Number of months
(a) Let's calculate the monthly deposit amount Jim must save each month to have $47,230 in 6 years.
First, we need to convert the annual interest rate to a monthly interest rate. The interest rate is given as 6% compounded monthly, so the monthly interest rate is 6% / 12 = 0.005.
Next, we calculate the number of months. Since Jim wants to have the money in 6 years, there are 6 years * 12 months/year = 72 months.
Now we can plug these values into the formula:
47,230 = P * ((1 + 0.005)^72 - 1) / 0.005
We can solve this equation for P:
P = 47,230 * 0.005 / ((1 + 0.005)^72 - 1)
Calculating this gives us:
P ≈ $539.66
Therefore, Jim must save approximately $539.66 each month to have $47,230 in 6 years.
(b) The amount Jim actually deposits is simply the monthly deposit amount multiplied by the number of months:
Deposit = P * n
Substituting the values we have:
Deposit = $539.66 * 72 = $38,889.52
To calculate the interest, we subtract the deposit from the total amount:
Interest = $47,230 - $38,889.52 = $8,340.48
So, Jim actually deposits $38,889.52, and the remaining $8,340.48 is the interest.