Answer:
Step-by-step explanation:
Formula to be used,
Final amount = [tex]\text{Initial amount}\times(1+\frac{r}{n})^{nt}[/tex]
r = rate of interest
n = number of compounding in a year
t = Duration of investment in years
Initial amount = $2000
r = 4% = 0.04
n = 4
A). Final amount = [tex]2000(1+\frac{0.04}{4})^{4\times 1}[/tex]
= 2000(1.01)⁴
= 2081.21
≈ $2081
B). If t = 18 months ≈ 1.5 years
Final amount = [tex]2000(1.01)^{4\times 1.5}[/tex]
= [tex]2000(1.01)^6[/tex]
= 2123.04
≈ $2123
C). If final amount = $25000
25000 = [tex]2000(1.01)^{4\times t}[/tex]
[tex]\frac{25}{2}=(1.01)^{4t}[/tex]
12.5 = [tex](1.040604)^t[/tex]
log(12.5) = [tex]\text{log}(1.040604)^t[/tex]
log(12.5) = t[log(1.040604)]
t = [tex]\frac{\text{log}(12.5)}{\text{log}(1.040604)}[/tex]
= 63.458
≈ 64 years
