Jessica plans to purchase a car in one year at a cost of $30,000. How much should be invested in an account paying 10% compounded semiannually to have the funds needed.
a. $27,210.90
b. $3,512.06
c. $24,793.50
d. $27,272.70
The Lee family plans to buy a new house in 2 years and wants to make a down payment of 25% of the estimated purchases price of $175,000. Find the amount they need to invest to make the down payment if funds earn 12% compounded semiannually.
a. $125,961.20
b. $34,653.94
c. $43,750
d. $138,615.75
Please help, show how you got the answers I get a better understanding. I have other questions like these. (These are example questions)
just refer to your compound interest formula.
#1: solve for P where
P(1+.10/2)^(2*1) = 30000
P = 27210.88
#2: same thing
P(1+.12/2)^(2*2) = .25*175000
To solve these problems, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
For the first question, Jessica plans to purchase a car in one year, and she needs $30,000. The interest rate is 10% compounded semiannually.
Let's solve for P:
$30,000 = P(1 + 0.10/2)^(2*1)
Simplifying the equation:
$30,000 = P(1.05)^2
Divide both sides by (1.05)^2:
P = $30,000 / (1.1025)
P ≈ $27,210.90
Therefore, Jessica should invest around $27,210.90 to have the funds needed. The correct answer is option a.
For the second question, the Lee family wants to make a down payment of 25% of the estimated purchase price of $175,000 in 2 years. The interest rate is 12% compounded semiannually.
Let's solve for P:
0.25 * $175,000 = P(1 + 0.12/2)^(2*2)
0.25 * $175,000 = P(1.06)^4
$43,750 = P(1.262476)
Divide both sides by (1.262476):
P = $43,750 / (1.262476)
P ≈ $34,653.94
Therefore, the Lee family needs to invest around $34,653.94 to make the down payment. The correct answer is option b.
I hope this explanation helps you understand how to solve these types of problems! If you have any more questions, feel free to ask.