Morgan deposits $500 every month into an account earning a monthly interest rate of 0.675% How many months would it be until Morgan had $13, 000 in the account, to the nearest month? Use the following formula to determine your answer.
A = d(((1 + i) ^ n - 1)/i)
A = the future value of the account after n periods d = the amount invested at the end of each period
i = the interest rate per period
First, we need to rearrange the formula to solve for n:
A = d(((1 + i) ^ n - 1)/i)
A = 13000
d = 500
i = 0.675% or 0.00675
13000 = 500(((1 + 0.00675) ^ n - 1)/0.00675
Next, we need to solve for n.
13000 = 500(((1.00675) ^ n - 1)/0.00675
13000 / 500 = ((1.00675) ^ n - 1)/0.00675
26 = ((1.00675) ^ n - 1)/0.00675
26 * 0.00675 = (1.00675) ^ n - 1
0.1755 = (1.00675) ^ n - 1
1.1755 = (1.00675) ^ n
n = log(1.1755) / log(1.00675)
n = 89.53
Therefore, it would take approximately 90 months for Morgan to reach $13,000 in the account.