Answer:
Option 3 is correct. After 18 years the amount will $3,875.79.
Step-by-step explanation:
The compound interest formula is
[tex]v(t)=p(1+\frac{r}{n})^{nt}[/tex]
Where, t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years.
The initial amount is $1,900. Interest rate is 4% and interest compounded semiannually. It means interest compounded 2 times in a year. The amount after t years is $3,875.79.
[tex]3,875.79=1900(1+\frac{0.04}{2})^{2t}[/tex]
[tex]3,875.79=1900(1.02)^{2t}[/tex]
[tex]\frac{3,875.79}{1900}=(1.02)^{2t}[/tex]
[tex]log(\frac{3,875.79}{1900})=log(1.02)^{2t}[/tex]
[tex]\frac{0.309606636902}{log(1.02)}=2t[/tex]
[tex]t=18[/tex]
After 18 years the amount will $3,875.79.
Therefore the option 3 is correct.
