Question

. Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compoundsmonthly. How much will the CD be worth in:6. 5 years? (round to the hundredths place)7. 10 years? (round to the hundredths place)8. How much will the CD be worth after 10 years using simple interest?

Answer 1

For this problem, we are informed about an investment made by Lori, they invested $1500 on an account that earns 6% interest compounded monthly. We need to find how much the account will be worth in 5 and 10 years. We also need to compare the value of the account in 10 years if it was a simple interest account.

In order to solve the compounded part of this problem, we need to use the following formula:

`A=P\cdot(1+(r)/(n))^(t\cdot n)`

Where A is the final amount, P is the invested principal, r is the interest rate, n is the number of times it gets compounded in a year, and t is the elapsed time.

For 5 years, we have:

`\begin{gathered} A=1500\cdot(1+(0.06)/(12))^(5\cdot12) \\ A=1500\cdot(1+0.005)^(60)_{} \\ A=1500\cdot(1.005)^(60) \\ A=2023.28 \end{gathered}`

For 10 years, we have:

`\begin{gathered} A=1500\cdot(1+(0.06)/(12))^(10\cdot12) \\ A=1500\cdot(1.005)^(120) \\ A=2729.1 \end{gathered}`

If the money were applied to an account with simple interest, we would need to use the following formula:

`A=P\cdot(1+rt)`

So for 10 years, we have:

`\begin{gathered} A=1500\cdot(1+0.06\cdot10) \\ A=1500\cdot(1+0.6)_{} \\ A=1500\cdot1.6 \\ A=2400 \end{gathered}`

If the money is invested for 5 years, the return is equal to 2023.28.

If the money is invested for 10 years, the return is equal to 2729.1.

If the money is invested for 10 years using simple interest, the return is equal to 2400.