Question

Your grandmother gives you $1500 to invest in a savings account on your 15th birthday. The only condition is that you may NOT use it until you have graduated high school at 18. After researching savings accounts, you come up with two options.1) A high interest savings account, with 2.5% simple interest annually or2) A High Yield Savings account with 2% interest compounded annually.Which account will you chose and why?

Answer 1

.Explanation.

To determine the best account to choose, we will have to check for the amount each account will yield

For the first account, with 2.5% simple interest annually

To find how much this account will yield at 2.5% simple interest annually, we will use the formula

`A=P+(P* R* T)/(100)`

Where

`\begin{gathered} p=\text{ \$1500} \\ r=2.5\text{ \%} \\ t=18-15=3years \end{gathered}`

Thus, the first account will yield

`\begin{gathered} A=1500+(1500*2.5*3)/(100) \\ \\ A=1500+15*7.5 \\ A=1500+112.5 \\ A=\text{ \$1612.5} \end{gathered}`

For the second account with 2% interest compounded annually

`\begin{gathered} A=P(1+(r)/(100))^t \\ where \\ P=1500 \\ r=2\text{ \%} \\ t=3 \end{gathered}`

Thus the account will yield

`\begin{gathered} A=1500(1+(2)/(100))^3 \\ A=1500(1.0612) \\ A=\text{ \$}1591.81 \end{gathered}`

We can see that the first account with 2.5% simple interest annually yields $1612.50 and

The second account with 2% interest compounded annually yields $1591.81

The difference in the accounts will be

`\text{ \$}1612.50-\text{ \$}1591.81=\text{ \$20.69}`

Thus, I will choose the first account with 2.5% simple interest annually, because it yields $20.69 more than the second account after 3 years