Answer: It will take 16 years to have a total of $15,000.
Step-by-step 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
[tex]15000 = 7890 (1+0.0565 \times t)[/tex] [ t = time ]
[tex]\dfrac{15000}{7980}=1+0.0565t\\\\\Rightarrow\ 0.0565t = \dfrac{15000}{7980}-1\\\\\Rightarrow\ 0.0565t =\dfrac{117}{133}\\\\\Rightarrow\ 0.0565t =0.87969924812\\\\\Rightarrow\ t=\dfrac{0.87969924812}{0.0565}\\\\\Rightarrow\ t=\dfrac{0.87969924812}{0.0565}\\\\\Rightarrow\ t\approx16\text{ years}[/tex]
Hence, it will take 16 years to have a total of $15,000.
