Solve the following word problem by using Table 11-2.
Stuart Daniels estimates that he will need $24,000 to set up a small business in 6 years. Round your answers to the nearest cent.
Click here for Table 11-2
a. How much must Stuart invest now at 8% interest compounded quarterly to achieve his goal?
$ _________
b. How much compound interest will he earn on the investment?
$ _________
reiny read my name
Stuart Daniels estimates that he will need $24,000 to set up a small business in 9 years.
(a)
How much (in $) must Stuart invest now at 8% interest compounded quarterly to achieve his goal?
$
(b)
How much compound interest (in $) will he earn on the investment?
$
To solve this word problem by using Table 11-2, we need to calculate the future value of an investment using compound interest. The formula to calculate the future value of an investment is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value (amount of money to invest now)
r = Interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Now, let's solve the problem:
a. To find out how much Stuart must invest now, we need to find the present value (PV) in the formula. We know the future value (FV) is $24,000, the interest rate (r) is 8%, and the investment period (t) is 6 years. We need to round the answer to the nearest cent.
Looking at Table 11-2, find the factor closest to the interest rate (8%) for the number of compounding periods (quarterly - 4 times a year) over the investment period of 6 years. The factor is 1.59385.
Now, we can apply the formula:
FV = PV * (1 + r/n)^(n*t)
$24,000 = PV * (1 + 0.08/4)^(4*6)
Divide both sides of the equation by the factor:
$24,000 / 1.59385 = PV
PV ≈ $15,054.47
Therefore, Stuart must invest approximately $15,054.47 at 8% interest compounded quarterly to achieve his goal.
b. To find the amount of compound interest Stuart will earn on the investment, subtract the initial investment (PV) from the future value (FV).
Compound Interest = FV - PV
Compound Interest = $24,000 - $15,054.47
Compound Interest ≈ $8,945.53
Therefore, Stuart will earn approximately $8,945.53 in compound interest on the investment.
Nobody uses "tables" any more, this is 2020
8% interest compounded quarterly ----> rate is .02 per quarter
6 year = 24 quarter years
x(1.02)^24 = 24000
This is the same type of question as your previous post