Kim deposits her annual bonus into a saving account that pays 8% interest compou

Question

Kim deposits her annual bonus into a saving account that pays 8% interest compounded annually. The size of her bonus increases by $2,000 each year, and the initial bonus amount is $5,000. Determine how much will be in the account immediately after the fifth deposit.

...I am using the formula for a linear gradient series. G(P/G,i,N) where the values at 8% are 0.8573 for N=2, 2.4450 for N=3, 4.6501for N=4, and 7.3724 for N=5.
...I am also using the formula for present worth. A(P/A,i,N) where the value at 8% are 1.7833 for N=2, 2.5771 for N=3, 3.3121 for N=4, and 3.9927 for N=5.

...My reasoning so far is...
P=$5,000(P/A,8,4) + $2,000(P/G,8,3)
=$16,560.5 + $4,890
= $21,450.5 (it seems like the answer should be greater than that...)

Explanation / Answer

so I found out how to do this on youtube but I got the correct answer using the interest factors

first know that A=A'+A" which means that A=5000+(A/G,8%,5)=8693

Now use (F/A,8%,5)*8693=$50998

I thought the other answer really didn't help with the correct method so I figured I'd share

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