Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The time for which the person must leave the money in the bank until it reaches $2500 is 1.2.
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
The principal amount is 1000 dollars, while the rate of interest is 6.75% which is compounded monthly. Therefore, the time it will need for the account to reach $2500 is,
2500 = 1000[1+(0.0675/12)¹²ˣⁿ
2.5 = (1.0675)¹²ⁿ
log(2.5)\ log(1.0675) = 12n
14.0278 = 12n
n = 1.1689 ≈ 1.2
Hence, the time for which the person must leave the money in the bank until it reaches $2500 is 1.2.
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