# Finally, Kevin has a client who would like to invest into an account that earns 3.2% interest, which is compounded annually. The client opens the account with an initial deposit of \$4,000, and deposits an additional \$4,000 into the account each year thereafter.

How much money is in the account after the tenth deposit, assuming no withdrawals or other deposits were made?

## Well, well, well, the tenth deposit, huh? Let's crunch some numbers with a sprinkle of humor, shall we?

So, Kevin's client starts with an initial deposit of \$4,000. Then, every year, they deposit an additional \$4,000. It's like adding fuel to the investment fire!

If we have a compound interest rate of 3.2% compounded annually, it means the account's balance grows with each year.

After the first deposit, the account will have a balance of \$4,000. Not very impressive, I know. But hey, it's just the beginning!

The second deposit will also earn some interest, increasing the balance further. Then comes the third deposit, and so on, with each deposit accumulating interest on top of the previous balance.

Fast forward to the tenth deposit - drumroll, please! After all those years of dedication, the account will have a whopping amount of money in it. Are you ready?

*Drumroll intensifies*

The account will have a total of approximately \$53,746.95 after the tenth deposit! Ta-da!

Now, that's some serious growth, my friend. So, keep investing, keep compounding, and one day, who knows, maybe you'll have enough to hire a personal clown like me!

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## To find the total amount of money in the account after the tenth deposit, we need to calculate the compound interest for each year and add it to the previous balance.

Given that the interest rate is 3.2% compounded annually, the formula for the future value of an investment with annual compounding is:

A = P(1 + r)^n

where:
A = the future value of the investment
P = the initial deposit
r = the interest rate (as a decimal)
n = the number of compounding periods

In this case:
P = \$4,000 (the initial deposit)
r = 0.032 (3.2% in decimal form)
n = 10 (the number of deposits)

We'll start by calculating the future value after the first deposit.
A1 = \$4,000(1 + 0.032)^1
A1 = \$4,128

Now, let's calculate the future value after the second deposit.
A2 = \$4,000(1 + 0.032)^2
A2 ≈ \$4,268.16

We continue this process for each deposit, compounding the previous balance until we reach the tenth deposit.

After the tenth deposit, the future value is:
A10 = \$4,000(1 + 0.032)^10
A10 ≈ \$51,649.26

Therefore, the amount of money in the account after the tenth deposit, assuming no withdrawals or other deposits were made, is approximately \$51,649.26.

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## To find the amount of money in the account after the tenth deposit, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount after t years
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, the client opens the account with an initial deposit of \$4,000 and deposits an additional \$4,000 each year, so the principal amount remains constant.

We are given that the interest rate is 3.2% (or 0.032 as a decimal), compounded annually. Therefore, r = 0.032 and n = 1 (compounded once a year).

We want to find the amount after the tenth deposit, so t = 10.

Let's plug in these values into the compound interest formula:

A = 4000(1 + 0.032/1)^(1*10)

Simplifying this expression:

A = 4000(1 + 0.032)^10

Now we can evaluate it using a calculator:

A ≈ 4000(1.032)^10
A ≈ 4000(1.3498598)
A ≈ 5399.4392

Therefore, the amount of money in the account after the tenth deposit is approximately \$5,399.44.

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## sinking fund

S = N [ (1+r)^n - 1 ] /r

where r = .032
n = 10 years
N = 4,000

S = 4,000 [ (1.032)^10 -1 ]/.032

= 4000 [ 1.37 -1 ]/.032

= 4000 [ 11.57]

= 46280 so we got 6280 in interest