You deposit $200 in a savings account.Each succeeding annual deposit is 3% higher.How much has been saved in your account immediately after you make your 20^th deposit if j₁ = 6%?

Question

Quizplus · Accepted Answer

Using the formula for the sum of a geometric series, we can find the total amount saved after 20 years:

$200(1 + 1.03 + 1.03^2 + \ldots + 1.03^{19}) = 200\frac{1 - 1.03^{20}}{1 - 1.03} = 5,986.28$

Now we need to find the value of the 20th deposit, which is 1.03 times the 19th deposit. We can set up a simple recursive equation:

$D_{20} = 1.03 D_{19}$

$D_{19} = 1.03 D_{18}$

$\vdots$

$D_2 = 1.03 D_1$

And we know that $D_1 = 200$.

So:

$D_{20} = 1.03^{19} D_1 = 200 (1.03^{19}) = 485.88$

Adding this to the total amount saved, we get:

$5,986.28 + 485.88 = 6,472.16$

Finally, we need to consider the interest earned on this amount. Using the compound interest formula, we get:

$6,472.16 (1 + 0.06) = 6,856.29$

Therefore, the answer is C.

You Deposit $200 in a Savings Account