Nancy would like to accumulate $10,000 by the end of 3 years from now to buy a used car from her friend,Jin. She has $2,500 now and would like to save equal annual end of year deposits to pay for the car.

Calculate how much should she deposit at the end of each year in an account pay 8% interest to buy the car at the end of 3 years.

Amount to save = 10,000-2500=7500

Use the future value formula:
A=F*(A/F,0.08,3)
=F(i)/((1+i)^n-1)
=7500*0.08/(1.08^3-1)
=2310.25

Note: each payment is even less than 7500/3=2500 because the first two payments earn interest at 8%.

Well, Nancy, it looks like you're in quite a pickle! Let's crunch some numbers and see how much you'll need to save.

First, let's take your current savings of $2,500. We'll need to grow that to $10,000 in 3 years, with an interest rate of 8%.

To calculate the annual deposits, we need to consider the interest that will be accumulating over the 3 years. By using the compound interest formula, we can determine how much you need to deposit every year to reach your goal.

Using the formula:

A = P(1 + r/n)^(nt),
where:
A = the future value of the investment,
P = the principal investment (the initial deposit),
r = annual interest rate (as a decimal),
n = number of times that interest is compounded per year, and
t = number of years

We plug in the values:
A = $10,000, P = $2,500, r = 8% (or 0.08 as a decimal), n = 1 (since it's an annual deposit), and t = 3.

10,000 = 2,500(1 + 0.08/1)^(1*3)

Now, we can solve for the annual deposit amount. But hold on to your clown wig, because here's where the math gets a bit clownish!

Let's simplify:

10,000 = 2,500(1.08)^3

10,000 = 2,500 * 1.259712

To find the annual deposit, we divide both sides by 1.259712:

10,000 / 1.259712 = 2,500

Voila! Your annual deposit should be approximately $7,942.22 (rounded to the nearest penny).

But remember, Nancy, this calculation doesn't account for any additional fees or fluctuations in the interest rate. So, keep an eye out for those clown cars on the road and stick to your savings plan!

To calculate how much Nancy should deposit at the end of each year, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + interest rate)^number of periods - 1] / interest rate

In this case, Nancy wants to accumulate $10,000 in 3 years. She already has $2,500, so she needs to save $10,000 - $2,500 = $7,500.

Since she wants to make equal annual deposits, we'll call the deposit amount "Payment".

The interest rate is given as 8% or 0.08, and the number of periods is 3 years.

Plugging these values into the formula:

$7,500 = Payment * [(1 + 0.08)^3 - 1] / 0.08

Simplifying:

$7,500 = Payment * (1.08^3 - 1) / 0.08
$7,500 = Payment * (1.2597 - 1) / 0.08
$7,500 = Payment * 0.2597 / 0.08
$7,500 = Payment * 3.24625

Now, let's solve for Payment:

Payment = $7,500 / 3.24625
Payment ≈ $2,310.22

Therefore, Nancy should deposit approximately $2,310.22 at the end of each year to accumulate $10,000 in 3 years with an 8% interest rate.

To determine how much Nancy should deposit at the end of each year, we can use the concept of annuities.

Step 1: Calculate the future value of the deposits:
Since Nancy wants to accumulate $10,000 by the end of 3 years, she already has $2,500, so she needs to save an additional $7,500 ($10,000 - $2,500).

Step 2: Use the formula for the future value of an annuity:
Future Value = Payment × [(1 + interest rate)^(number of periods) - 1] / interest rate

In this case, the future value is $7,500, the interest rate is 8%, and the number of periods is 3. Let's plug these values into the formula:

$7,500 = Payment × [(1 + 0.08)^(3) - 1] / 0.08

Simplifying this equation, we get:

$7,500 = Payment × [(1.08)^3 – 1] / 0.08

Step 3: Calculate the value inside the brackets:

(1.08)^3 – 1 = (1.259712) – 1 = 0.259712

Step 4: Rearrange the formula to solve for the Payment:

Payment = $7,500 × 0.08 / 0.259712

Payment = $2,304.54

Therefore, to accumulate $10,000 by the end of 3 years, Nancy would need to deposit approximately $2,304.54 at the end of each year in an account paying 8% interest.