wendy invests $500 into a savings account with interest that compounds annually at a rate of 2.5%. write a model that shows the total amount of money in her account as a function of time. how much money show wendy expect ri have in her savings account after 6 years. assuming she does not deposit or withdraw any other money before that time. compound interest:A=P(1+ r/n)^nt
To calculate the total amount of money in Wendy's account as a function of time, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the total amount of money in the account after t years
P = the initial investment (principal), which is $500 in this case
r = the annual interest rate in decimal form, which is 2.5% or 0.025
n = the number of times the interest is compounded per year (annually in this case)
t = the number of years
Plugging in the values into the formula, we have:
A(t) = 500(1 + 0.025/1)^(1*6)
= 500(1.025)^(6)
≈ $538.63
Therefore, Wendy can expect to have approximately $538.63 in her savings account after 6 years, assuming she does not make any additional deposits or withdrawals.