Question

If you invest $7,890 at a 5.65% simple annual interest rate, approximately how long will it take for you to have a total of $15,000? Show work

Answer 1

Answer: It will take 16 years to have a total of $15,000.

Explanation:

Given : Principal value = $ 7,890

Rate of interest = 5.65 % = 0.0565

Amount = $ 15000

Interest = Principal x Rate x time

Amount = Principal + Interest

Amount = Principal + Principal x Rate x time

Amount = Principal ( 1 + Rate x time )

Substitute values, we get

`15000 = 7890 (1+0.0565 * t)` [ t = time ]

`(15000)/(7980)=1+0.0565t\\\\\Rightarrow\ 0.0565t = (15000)/(7980)-1\\\\\Rightarrow\ 0.0565t =(117)/(133)\\\\\Rightarrow\ 0.0565t =0.87969924812\\\\\Rightarrow\ t=(0.87969924812)/(0.0565)\\\\\Rightarrow\ t=(0.87969924812)/(0.0565)\\\\\Rightarrow\ t\approx16\text{ years}`

Hence, it will take 16 years to have a total of $15,000.