QuestionCalculate the monthly deposit needed to reach \$85,000 in 18 years with a 6% APR.

Studdy Solution

STEP 1

Assumptions1. The goal is to accumulate $85,000. The annual interest rate (APR) is6%
3. The time for accumulation is18 years4. The interest is compounded monthly5. The same amount is deposited every month

STEP 2

First, we need to convert the annual interest rate to a monthly interest rate. We can do this by dividing the annual interest rate by12.
$Monthly\, interest\, rate = Annual\, interest\, rate /12$

STEP 3

Now, plug in the given value for the annual interest rate to calculate the monthly interest rate.
$Monthly\, interest\, rate =6\% /12$

STEP 4

Convert the percentage to a decimal value.
$6\% =0.06$ $Monthly\, interest\, rate =0.06 /12$

STEP 5

Calculate the monthly interest rate.
$Monthly\, interest\, rate =0.06 /12 =0.005$

STEP 6

Next, we need to find the total number of months. We can do this by multiplying the number of years by12.
$Total\, months = Years \\times12$

STEP 7

Now, plug in the given value for the number of years to calculate the total number of months.
$Total\, months =18 \\times12$

STEP 8

Calculate the total number of months.
$Total\, months =18 \\times12 =216$

STEP 9

We can now use the savings plan formula to find the monthly deposit. The formula is $Monthly\, deposit = Total\, amount / (( + Monthly\, interest\, rate)^{Total\, months} -) / Monthly\, interest\, rate$

STEP 10

Plug in the values for the total amount, the monthly interest rate, and the total number of months to calculate the monthly deposit.
$Monthly\, deposit = \$85,000 / (( +0.005)^{216} -) /0.005$

STEP 11

Calculate the monthly deposit amount.
$Monthly\, deposit = \$85,000 / (( +0.005)^{216} -) /0.005 = \$198.65$ You should deposit approximately $198.65 each month.

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