Ruby opens a savings account, with the goal of saving $20,000 by making deposits each month for the next 10 years. If the account pays 1.5% interest, how much should Ruby deposit each month?

Question

$23,234.51
$166.67
$179.58
$17,215.77
$154.58

Answer 1

To calculate how much Ruby should deposit each month, we can use the future value of an annuity formula:

FV = Pmt * [(1 + r)^n - 1] / r

Where:
FV = Future value of the savings account ($20,000)
Pmt = Monthly deposit
r = monthly interest rate (1.5%/12 = 0.00125)
n = number of months (10*12 = 120)

Plugging in the values:

$20,000 = Pmt * [(1 + 0.00125)^120 - 1] / 0.00125
$20,000 = Pmt * (1.00125^120 - 1) / 0.00125
$20,000 = Pmt * (1.2039 - 1) / 0.00125
$20,000 = Pmt * 0.2039 / 0.00125
$20,000 = Pmt * 163.12
Pmt = $20,000 / 163.12
Pmt ≈ $122.63

Therefore, Ruby should deposit approximately $122.63 each month in order to reach her goal of saving $20,000 in 10 years. None of the options provided match this calculation, so a new calculation is required. Let's try again:

PV = Pmt * [(1 - (1 + r)^-n) / r]

$20,000 = Pmt * [(1 - (1 + 0.00125)^-120) / 0.00125]
$20,000 = Pmt * [(1 - 0.812824) / 0.00125]
$20,000 = Pmt * 630.14
Pmt = $20,000 / 630.14
Pmt ≈ $31.74

Therefore, Ruby should deposit approximately $31.74 each month in order to reach her goal of saving $20,000 in 10 years. None of the options provided match this calculation. Let's try once again:

Pmt = (FV * r) / [(1 + r)^n - 1]

Pmt = ($20,000 * 0.00125) / (1.00125^120 - 1)
Pmt = $25 / (1.2039 - 1)
Pmt = $25 / 0.2039
Pmt = $122.74

Therefore, Ruby should deposit approximately $122.74 each month in order to reach her goal of saving $20,000 in 10 years. Unfortunately, this value does not match any of the options provided. It's possible there was an error in the calculations, but the correct approximate monthly deposit amount should be around $122.74.