Answer:
It will take 35.46 quarters for the account to grow to $3000.
Step-by-step explanation:
Since the annual rate is compounded quarterly, this can be calculated using the formula for calculating the future value as follows:
FV = PV * (1 + r)^n ............................ (1)
Where;
FV = future value or the amount the deposit expected to grow to = $3,000
PV = Present value or the amount place in the savings = $2,000
r = Quarterly rate = Annual rate / 4 = 4.6% / 4 = 0.046 / 4 = 0.0115
n = number of quarters it will take for the loan to grow to $3000 = ?
Substituting the values into equation (1) and solve for n, we have:
$3,000 = $2,000 * (1 + 0.0115)^n
$3,000 / $2,000 = (1.0115)^n
1.50 = (1.0115)^n
Loglinearise both sides, we have:
log(1.50) = n log(1.0115)
0.176091259055681 = n * 0.00496588710682352
n = 0.176091259055681 / 0.00496588710682352
n = 35.4601816891322
Rounding to the nearest hundredth, which also implies to rounding to 2 decimal places, we have:
n = 35.46
Since the the annual rate is compounded quarterly, it will therefore take 35.46 quarters for the account to grow to $3000.
is 5 times
, which means
, so we have
. This means that
So, substituting this back gives