Respuesta :
Answer:
$53,635
Explanation:
The question is to calculate the future value of the $100 that is being deposited monthly for 18 years
The formula for the Future value of the deposits is as follows:
FV= P [ ( (1 + r/n)∧ n * Y -1) / r/n) ]
Where P Deposited amount per month= $100
r= Interest rate 9%
n= the number of deposits made in a year = 12
Y= the number of years=18
Based on the formula
FV= $100 ( ( 1+0.09/1200)∧ 12 * 18 -1) / 0.09/1200) ]
FV= $100 [ ( 1.0075∧ 216 -1) / 0.0075]
FV= $100 [( 5.022-1/) 0.0075]
FV= $100 (4.022/0.0075)
FV = $100 x 536.35
FV= $53,635
The amount of money in my savings account will be closest to $54,037.43.
In order to determine the future value with monthly deposits, this formula would be used:
FV = [tex]d * \frac{( 1 + i)^{t} - 1 }{i} * (1 + i)[/tex]
- FV = future value of the deposit
- i = interest rate = 9% /12 = 0.75%
- t = time = 18 x 12 = 216
- d = monthly deposits = $100
[tex]100 * \frac{(1.0075)^{216} - 1 }{0.0075} * (1.0075)[/tex] = $54,037.43
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