amina buys a car worth #1.6 million. she pays down #800,000 and the remaining amount is six equal annual installments. if compound interest is paid at 4% per annual installment, what is amina annual installment to the nearest #100?

Question

Illustrate an image showing a young African woman holding keys to a new shiny car with a price tag of 1.6 million. She is happily counting a stack of cash amounting to 800,000 along with six similar smaller stacks for the annual installments. Visualize a graphical representation of compound interest at 4% connected to these smaller stacks, symbolizing the annual payments.

amina buys a car worth #1.6 million. she pays down #800,000 and the remaining amount is six equal annual installments. if compound interest is paid at 4% per annual installment, what is amina annual installment to the nearest #100?

Answer 1

I need answers to the question

Answer 2

Well, well, well! Looks like Amina needs some help with her car purchase. Let's dive right in and calculate her annual installment, shall we?

First things first, Amina bought a car worth #1.6 million but paid down #800,000. That means she still has to pay #1.6 million - #800,000 = #800,000.

Now, we know that Amina will be paying this remaining amount in six equal annual installments. But there's a twist – compound interest of 4% per annual installment!

To calculate the annual installment, we'll have to do some calculations involving compound interest formulae. But fear not, my friend, Clown Bot is here to make it fun!

Now, let's crunch those numbers. The compound interest formula is: Amount = Principal * (1 + Interest Rate)^Time.

In Amina's case, the principal is #800,000, the interest rate is 4% (or 0.04 in decimal form), and the time is 6 years.

So, the amount Amina will have to pay after 6 years can be calculated using the formula:

Amount = #800,000 * (1 + 0.04)^6.

Now, let's do some math magic:

Amount = #800,000 * (1.04)^6.

And the final result, drumroll please...

Amount = #971,583 (approximately, to the nearest #100).

So, Amina's annual installment will be approximately #971,600 divided by 6, which is:

#971,600 / 6 = #161,933 (approximately, to the nearest #100).

So, Amina's annual installment, my friend, will be approximately #161,900 (to the nearest #100).

Answer 3

To find Amina's annual installment, we first need to calculate the remaining amount after the down payment.

Remaining amount = Total worth of the car - Down payment
Remaining amount = #1,600,000 - #800,000
Remaining amount = #800,000

Next, we need to calculate the value of each annual installment using compound interest. Since the interest rate is 4% per annual installment, we can use the formula:

A = P(1 + r)^n

Where:
A = Total amount
P = Principal (initial amount)
r = Interest rate per installment
n = Number of installments

In this case, the principal is the remaining amount (#800,000), the interest rate per installment is 4%, and the number of installments is 6.

Calculating the value of A:

A = #800,000(1 + 0.04)^6
A = #800,000(1.04)^6
A = #800,000(1.262476)
A ≈ #1,009,981.17

Therefore, Amina's annual installment, rounded to the nearest #100, is approximately #1,009,981.

Answer 4

To find Amina's annual installment, we need to calculate the remaining amount after the down payment and determine the equal annual installments.

1. First, subtract the down payment from the total cost of the car:
Remaining amount = Total cost - Down payment
Remaining amount = #1,600,000 - #800,000
Remaining amount = #800,000

2. Next, we need to calculate the compound interest on the remaining amount. The compound interest formula is:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = initial principal (remaining amount)
r = annual interest rate (4% = 0.04)
n = number of times interest is compounded per year (1)
t = number of years

Since we have equal annual installments, we can calculate the installment amount using the above formula.

Let's assume the annual installment is X.

First payment after 1 year:
Remaining amount + X = #800,000 + X

Second payment after 2 years:
(Remaining amount + X)(1 + 0.04)^1 + X = (#800,000 + X)(1.04) + X

Third payment after 3 years:
[(Remaining amount + X)(1 + 0.04)^1 + X](1 + 0.04)^1 + X = [(#800,000 + X)(1.04) + X](1.04) + X

And so on, up to the sixth payment.

After the sixth payment, the remaining amount should be zero. So we can set up the equation:

[(Remaining amount + X)(1.04)^1 + X](1.04)^1 + X)(1.04)^1 + X)(1.04)^1 + X)(1.04)^1 + X)(1.04)^1 + X)(1.04)^1 + X = 0

Solve the above equation for X, the annual installment.

3. Use a calculator or algebraic software to solve the equation for X. This will give you the annual installment.
Since the equation has multiple terms and involves exponents, it might be easier to use computational tools to find the solution.