What is the future value at the end of year 20 of depositing $5,000 today, $3,500 at the end of years 1,

2 and 3, $5,000 at the end of years 4, 5, 6 and 7 and $4,250 at the end of years 8, 9, 10, 11 and 12 into
an account that pays 13% p.a.?

It's tedious, but there isn't a useful shortcut.

In year one, you add 13% of 5000 to the 5000, making 5650. Then you add 3500, making 9150. Then you add 13% to that, and then add another 3500, and go for another year @ 13%. And so on.

can I plug this in on a financial calculator? If so how would I?

To calculate the future value of the given deposits, we can use the formula for future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:
FV = Future value
P = Periodic payment
r = Interest rate per period
n = Number of periods

Let's break down the given deposits and calculate the future value step by step.

1. Deposit $5,000 today:
FV1 = $5,000 * ((1 + 0.13)^20 - 1) / 0.13

2. Deposits of $3,500 at the end of years 1, 2, and 3:
FV2 = $3,500 * ((1 + 0.13)^3 - 1) / 0.13

3. Deposits of $5,000 at the end of years 4, 5, 6, and 7:
FV3 = $5,000 * ((1 + 0.13)^4 - 1) / 0.13

4. Deposits of $4,250 at the end of years 8, 9, 10, 11, and 12:
FV4 = $4,250 * ((1 + 0.13)^5 - 1) / 0.13

Finally, to get the total future value, we can add up all the calculated values:

Total Future Value = FV1 + FV2 + FV3 + FV4

Now, you can substitute the values and calculate the result.