Barbara knows that she will need to buy a new car in 4 years. The car will cost $15,000 by then. How much should she invest now at 10%, compounded quarterly, so that she will have enough to buy a new car? Round to the nearest cent.
solve for x
x(1.025)^16 = 15000
im not sure how to complete the problem becuase my answer was 9312.82, not sure if this is correct
I have no idea how you got that.
I am using the standard formula
Amount = principal(1 + i)^n
where i is the periodic interest rate, and n is the number of interest periods
the rate is 10% p.a., compounded quarterly , so i = .10/4 = .025
and the time is 4 years or 16 quarter years, hence n = 16
so
x(1.025)^16 = 15000
x(1.484505621) = 15000
http://www.google.ca/search?hl=en&source=hp&q=1.025%5E16&meta=&aq=f&aqi=&aql=&oq=&gs_rfai=
x = 15000/1.484505621
= 10104.37
http://www.google.ca/search?hl=en&source=hp&q=1.025%5E16&meta=&aq=f&aqi=&aql=&oq=&gs_rfai=
ok i get it , thanks
To determine how much Barbara should invest now, we need to calculate the present value of $15,000 at a 10% annual interest rate, compounded quarterly, over a period of 4 years.
The formula to calculate the present value, also known as the principal value, is:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value (amount to be invested now)
FV = Future Value (amount needed to buy the car)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case:
FV = $15,000
r = 10% or 0.10 (as a decimal)
n = 4 (compounded quarterly)
t = 4 years
Plugging in these values into the formula, we have:
PV = $15,000 / (1 + 0.10/4)^(4*4)
Step 1: Simplify the expression inside the parentheses.
PV = $15,000 / (1.025)^(16)
Step 2: Calculate the exponent.
(1.025)^(16) ≈ 1.431046872
Step 3: Divide the future value by the present value factor.
PV ≈ $15,000 / 1.431046872
PV ≈ $10,485.17
Therefore, Barbara should invest approximately $10,485.17 now at a 10%, compounded quarterly, to have enough to buy a new car in 4 years.