QuestionDeposit $\$ 5000$ at $7\%$ interest compounded monthly. What is the total in 10 years?

Studdy Solution

STEP 1

Assumptions1. The initial deposit is $\$5000$ . . The annual interest rate is $7\%$ .
3. The interest is compounded monthly.
4. The time for the deposit is10 years.

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.
$Monthly\, interest\, rate =7\% /12$

STEP 4

Convert the percentage to a decimal value.
$7\% =0.07$ $Monthly\, interest\, rate =0.07 /12$

STEP 5

Calculate the monthly interest rate.
$Monthly\, interest\, rate =0.07 /12 =0.00583$

STEP 6

Now that we have the monthly interest rate, we can find the total amount in the account after10 years. This can be calculated using the formula for compound interest $Total\, amount = Principal\, amount \\times (1 + Monthly\, interest\, rate)^{Number\, of\, months}$

STEP 7

First, calculate the number of months in10 years.
$Number\, of\, months =10 \\times12 =120$

STEP 8

Now, plug in the values for the principal amount, monthly interest rate, and number of months into the formula to calculate the total amount.
$Total\, amount = \$5000 \\times (1 +0.00583)^{120}$

STEP 9

Calculate the total amount in the account after years.
$Total\, amount = \$500 \\times ( +.00583)^{120} = \$,244.70$ After years, you will have $,244.70 in the account.

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