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 answer and include appropriate units
50000(1+.069/4)^(4*15) = 139518
so he'll be short.
Thanks Steve!
To determine if Ron will reach his goal of $150,000 in 15 years by investing $50,000 in an account paying 6.19% interest compounded quarterly, 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 = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Given:
P = $50,000
r = 6.19% = 0.0619
n = 4 (compounded quarterly)
t = 15 years
Let's plug in the values and calculate:
A = 50000(1 + 0.0619/4)^(4*15)
A ≈ 118961.68
After evaluating the equation, we find that the future value of the investment is approximately $118,961.68.
Since $118,961.68 is less than Ron's goal of $150,000, it means he will not reach his goal in 15 years by investing $50,000 with this interest rate and compounding frequency.