Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The number of years it will take for $390 to become $660 is 9.63 years.
What is compound interest?
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
Given the principal amount is $390, the rate of interest is 5.5%(0.055), the number of times the interest is charged in a year (n=4), and the final amount is $660, therefore, the number of years will be equal to,
[tex]660 = 390(1+ \dfrac{0.055}{4})^{4 \times t}\\\\\dfrac{660}{390} = (1.01375)^{4 \times t}\\\\1.6923 =(1.01375)^{4 \times t}\\\\{\rm log}_{1.01375}1.6923 = 4t\\\\4t = 38.5234\\\\t=9.63[/tex]
Hence, the number of years it will take for $390 to become $660 is 9.63 years.
Learn more about Compound Interest:
https://brainly.com/question/25857212
#SPJ2
