Jasica Parker would like to have $78 comma 000
to buy a new car in 8
years. To accumulate $ 78 comma 000
in 8
years, how much should she invest monthly in a sinking fund with 6 %
interest compounded monthly?
$78 comma 000 ????
Why not just say $78,000 ?
i = .06/12 = .005
n = 12(8) = 96
paym( 1.005^96 - 1)/.005 = 78000
solve for paym
To calculate how much Jasica Parker should invest monthly in a sinking fund with 6% interest compounded monthly, we need to use the principle of compound interest formula.
The formula to calculate the future value of an investment with compound interest is:
FV = P(1 + r/n)^(nt)
Where:
FV = Future value of the investment
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, Jasica wants to accumulate $78,000 in 8 years, with a 6% annual interest compounded monthly. Let's break down the variables according to the given values:
FV = $78,000
P = ?
r = 6% = 0.06 (in decimal form)
n = 12 (compounded monthly)
t = 8 years
Plugging in these values into the formula, we get:
$78,000 = P(1 + 0.06/12)^(12*8)
Now, we solve for P:
P = $78,000 / (1 + 0.06/12)^(12*8)
Calculating the above expression should give us the monthly investment amount that Jasica needs to make.