210k views
1 vote
Landry is opening two savings accounts. He is opening the first account with an initial deposit of $500. The account will compound continuously each year at a rate of 3%.

He is opening the second account with an initial deposit of $300. The account will compound continuously each year at a rate of 5%.

Landry would like to know how long it will take for the balance of the two accounts to be equal.

Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.

2 Answers

4 votes

Answer:

Never. (Not viable)

Explanation:

3% of 500=15

5% of 300=15

Since both of them would get $15 a year, then they would stay the same amount apart. For example, when the first account reached 515 dollars, the second one would be at 315 dollars. Thus, they'd always be 200 dollars apart.

However!

Since it is a compound interest, and if there is the original 7% a year, the formula we'll use for this is the simple interest formula, or:

I=Pxrxt

Where:

P is the principal amount, $500.00.

r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 500 × 0.03 × 5 to get that:

The interest is: $75.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),

or 500.00 + 75.00 = 575.00. For example:

If you borrowed the $500.00, you would now owe $575.00

If you loaned someone $500.00, you would now be due $575.00

If owned something, like a $500.00 bond, it would be worth $575.00 now.

You want to calculate the interest on $300 at 5% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:

I=Pxrxt

Where:

P is the principal amount, $300.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 300 × 0.05 × 5 to get that:

The interest is: $75.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),

or 300.00 + 75.00 = 375.00. For example:

If you borrowed the $300.00, you would now owe $375.00

If you loaned someone $300.00, you would now be due $375.00

If owned something, like a $300.00 bond, it would be worth $375.00 now.

4 votes

Answer: there is only one solution and it is viable . ( answer on PLATO)

Explanation:

User Lanayx
by
6.3k points