Question

Question 3
Imagine that you deposit
$
6
,
000
$6,000 a year, starting one year from today, for four years into a savings account paying
6
%
6% per annum.

(That is one deposit of
$
6
,
000
$6,000 per year.)

How much money will you have immediately after you make your fourth and final deposit?


27
,
822.56
27,822.56



24
,
000
24,000



26
,
247.70
26,247.70



30
,
299.44
30,299.44

Answer 1

To calculate the amount of money you'll have immediately after making your fourth and final deposit into a savings account that pays 6% interest per annum, we can treat each deposit separately, as they will each accumulate interest for different lengths of time.

Here's the breakdown:

1. **First Deposit**: $6,000 will be in the account for 3 years (it will earn interest for the next 3 years).
\[
FV = 6000 \times (1 + 0.06)^3
\]
\[
FV = 6000 \times (1.191016) \approx 7146.096
\]

2. **Second Deposit**: $6,000 will be in the account for 2 years.
\[
FV = 6000 \times (1 + 0.06)^2
\]
\[
FV = 6000 \times (1.1236) \approx 6741.6
\]

3. **Third Deposit**: $6,000 will be in the account for 1 year.
\[
FV = 6000 \times (1 + 0.06)^1
\]
\[
FV = 6000 \times (1.06) = 6360
\]

4. **Fourth Deposit**: $6,000 will not earn any interest as it's deposited at the end of year 4.
\[
FV = 6000
\]

Now, we can sum all the future values to find the total amount immediately after the fourth deposit:

\[
7146.096 + 6741.6 + 6360 + 6000 = 26,247.696
\]

Rounding to two decimal places:

\[
\approx 26,247.70
\]

Therefore, you will have **$26,247.70** immediately after you make your fourth and final deposit.

So the answer is:
**26,247.70**.