Jaya deposits $820 every month into an account earning an annual interest rate of 5.7% compounded monthly. How much would she have in the account after 9 years, to the nearest dollar?
To calculate the future value of Jaya's account after 9 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the account
P = the monthly deposit of $820
r = the annual interest rate of 5.7% (or 0.057 as a decimal)
n = the number of times the interest is compounded per year (monthly compounding means n = 12)
t = the number of years
Plugging in the values:
A = 820(1 + 0.057/12)^(12*9)
A = 820(1 + 0.00475)^108
A = 820(1.00475)^108
A = 820(1.6488533)
A = $1351.304676
Rounding to the nearest dollar, Jaya would have approximately $1,351 in the account after 9 years.