Answer:
The Amount after 4 years is $2430 .
Step-by-step explanation:
Given as :
The principal amount investment = p = $2000
The rate of interest applied = r = 5%
The time for investment = t years
Let The Amount after t years = $A
<u>From Compound Interest method</u>
Amount = Principal × ![(1+\dfrac{\textrm rate}{100})^{\textrm time}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20rate%7D%7B100%7D%29%5E%7B%5Ctextrm%20time%7D)
Or, A = p × ![(1+\dfrac{\textrm r}{100})^{\textrm t}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20r%7D%7B100%7D%29%5E%7B%5Ctextrm%20t%7D)
Or, A = $2000 × ![(1+\dfrac{\textrm 5}{100})^{\textrm t}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%205%7D%7B100%7D%29%5E%7B%5Ctextrm%20t%7D)
Or, A = $2000 × ![(1.05)^{\textrm t}](https://tex.z-dn.net/?f=%281.05%29%5E%7B%5Ctextrm%20t%7D)
So, The Amount after t years = A = $2000 × ![(1.05)^{\textrm t}](https://tex.z-dn.net/?f=%281.05%29%5E%7B%5Ctextrm%20t%7D)
B) The principal amount investment = p = $2000
The rate of interest applied = r = 5%
The time for investment = t = 4 years
Let The Amount after t years = $A
<u>From Compound Interest method</u>
Amount = Principal × ![(1+\dfrac{\textrm rate}{100})^{\textrm time}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20rate%7D%7B100%7D%29%5E%7B%5Ctextrm%20time%7D)
Or, A = p × ![(1+\dfrac{\textrm r}{100})^{\textrm t}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20r%7D%7B100%7D%29%5E%7B%5Ctextrm%20t%7D)
Or, A = $2000 × ![(1+\frac{5}{100})^{4}](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7B5%7D%7B100%7D%29%5E%7B4%7D)
Or, A = $2000 × ![(1.05)^{4}](https://tex.z-dn.net/?f=%281.05%29%5E%7B4%7D)
i.e A = $2000 × 1.215
Or, A = $2430
So, The Amount after 4 years = A = $2430
Hence, The Amount after 4 years is $2430 . Answer