Ron would like to have at least $150,000 saved to buy a condo. If he invests $50,000 in an account paying 6.19% interest compounded quarterly, will he reach his goal in 15 years? Show all work to justify your answer and include appropriate units.
150000 = 50000 [1 + (.0619 / 4)]^(y * 4)
3 = [1 + (.0619 / 4)]^(4y)
log(3) = 4y log[1 + (.0619 / 4)]
Thanks Scott!
Thanks Scott! Could you possibly break the format down a little more? Did he reach his goal and the units.
To determine if Ron will reach his goal of saving $150,000 in 15 years by investing $50,000 in an account with a 6.19% interest rate compounded quarterly, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
Given:
P = $50,000
r = 6.19% or 0.0619 (as a decimal)
n = 4 (quarterly compounding)
t = 15 years
Substituting the values into the formula:
A = $50,000(1 + 0.0619/4)^(4 * 15)
Calculating the equation step by step:
A = $50,000(1 + 0.015475)^(60)
A = $50,000(1.015475)^(60)
A = $50,000 * 1.86719800675
A = $93,359.90
After 15 years with an investment of $50,000 at a 6.19% interest rate compounded quarterly, Ron would have approximately $93,359.90. This falls short of his goal of $150,000.
Therefore, Ron will not reach his goal of $150,000 in 15 years by investing $50,000 in an account with a 6.19% interest rate compounded quarterly.