Suzy deposits $500 in a savings account with an interest rate of 6% compounded annually. if suzy does not make any additional deposits or withdrawals, how long will it take for suzy to earn at least $95
for y being the time in years
595 = 500 (1 + .06)^y
log(595 / 500) = y log(1.06)
To find out how long it will take for Suzy to earn at least $95, we will need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after time t
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time in years
In this case, Suzy deposits $500 (P), earns an interest rate of 6% (r = 0.06), compounded annually (n = 1), and wants to find out how long it will take for the amount to be at least $595 ($500 + $95).
Substituting these values into the formula, we get:
595 = 500(1 + 0.06/1)^(1*t)
Now, let's solve for t:
595/500 = (1 + 0.06)^t
1.19 = 1.06^t
Taking the logarithm of both sides, we get:
log(1.19) = log(1.06^t)
t * log(1.06) = log(1.19)
t = log(1.19) / log(1.06)
Using a calculator, we find that:
t ≈ 5.96 years
So, it will take approximately 5.96 years for Suzy to earn at least $95 in interest on her deposit of $500.