Question

Marcy has a savings account that started with $1500 and receives 3.8% compounded quarterly for 10 years. What is the value of her account of the time period?

What is the correct form of the interest rate that would be used in the interest formula?

Answer 1

The money in her savings account will be $2188.5 after 10 years.

Explanation:

It is given that,

• The amount deposited is $1500.
• The account receives 3.8% interest compounded quarterly.
• It is compounded for 10 years.

To find the money in the account after 10 years :

The formula used here is,

⇒
`A = P(1+r/n)^(nt)`

where A is the amount after 10 years.

• P is the initial amount deposited ⇒ P = 1500
• r is the rate ⇒ r = 3.8/100 = 0.038

The correct form of the interest rate converted from % to decimal form by dividing the rate with 100.

• n is the number of times interest is compounded per year⇒ n = 4
• t is the time period ⇒ t = 10

⇒
`1500(1+0.038/4)^(10* 4)`

⇒
`1500(4.038/4)^(40)`

⇒
`1500*1.0095^(40)`

⇒
`1500 * 1.459`

⇒
`2188.5`

Therefore, The money in her savings account will be $2188.5 after 10 years.