Question

A philanthropist deposits $4,000 in a trust fund that pays 5.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 40 years. How much will the college receive?

Answer 1

They will receive 8,800$

Explanation:

4000x0.055=220

220x40=$8,800

Answer 2

The college will receive approximately $36,824.32 after 40 years.

To solve this problem

We can use the formula for continuous compound interest:

`A = P * e^(^r^t^)`

Where

• A is the total sum.
• P stands for principle (deposit) initially.
• e is equal to Euler's number, or around 2.71828.
• The interest rate, expressed in decimal form, is r.
• t is the number of years.

In this case, the initial principal (P) is $4,000, the interest rate (r) is 5.5% (or 0.055 as a decimal), and the time (t) is 40 years.

Plugging in the values into the formula, we have:

`A = 4000 * e^(^0^.^0^5^5^ * ^4^0^)`

Now, we can evaluate
`e^(^0.^0^5^5^ *^ 4^0)` to approximately 2.71828^(2.2) which is roughly 9.206

So, the final amount (A) that the college will receive is:

A = 4000 * 9.206 = $36,824.32

So, the college will receive approximately $36,824.32 after 40 years.