Final answer:
By calculating compound interest, the balance obtained after 25 years of investing $900 at a 4.6% rate with monthly compounding is $2,919.26.
Step-by-step explanation:
The question asks for the balance after 25 years when $900 is invested at a rate of 4.6% with monthly compounding. To find this balance, we can use the formula for compound interest:
A = P (1 + \( \frac{r}{n} \))^nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount ($900).
r is the annual interest rate (decimal) (4.6% or 0.046).
n is the number of times that interest is compounded per year (12 for monthly).
t is the time the money is invested for (25 years).
So,
A = 900 (1 + \( \frac{0.046}{12} \))^(12\times25)
By calculating the compound interest, we find that the balance after 25 years would be:
A = $900 (1 + 0.00383333)^300
A = $900 (1.00383333)^300
A = $900 \times 3.2436242
A = $2,919.26 (after rounding to the nearest cent)
The balance after 25 years would be $2,919.26.