1. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
thank you so much!
+128475 We have the following "formula"
A = P ( 1 + r)^t
Where
A = 800
P = 500
r = 1.5% = .015
And we are looking for t
So we have
800 = 500 ( 1 + .015)^t divide both sides by 500
(800/500) = (1 + .015)^t
(8/5) = (1.015)^t take the log of both sides
log (8/5) =log (1.015)^t and we can write
log(8/5) = t * log (1.015) divide both sides by log(1.015)
log(8/5) /log (1.015) = t ≈ 31. 57 yrs = 32 years (to the nearest year)
