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8_murik_8 [283]
3 years ago
6

A prize fund is setup with a single investment of £4000 to provide an annual prize of £150. The fund accrues interest at 5% p.A.

Paid yearly. If the first prize is awarded one year after the investment, find the number of years for which the full prize can be awarded.
Mathematics
1 answer:
Verdich [7]3 years ago
7 0

The invested amount, A=£4000

Rate of interest on this amount, r=5% per annum.

Total interest on the amount £4000 after 1 year

= 5\% \;\text{of} \;\£ 4000=0.05\times \£4000=\£200.

The total amount after 1 year, P=£4000+£200=£4200

Amount remains after an annual prize of £150=£4200-£150=£4050.

Note that after providing the annual prize the amount remains is £4050 which is more than the invested amount of £4000 as the prize money is less than the interest gained.

Now, for the 2nd year, the 5% interest is on the principal amount of £4050, which will have more interest as compared to the interest of 1st year.

Again, after prize distribution, the total amount remains for the principal amount of 3rd year will be more than the principal amount of 2nd year. This sequence repeated every year and the total amount will increase every year.

So, it will never end, the full prize money can be awarded for infinitely many years.

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6 0
3 years ago
Find the geometric mean between each pair of numbers. sq root 49 and sq root841
vodomira [7]

<u>Answer:</u>

The geometric mean between each pair of numbers \bold{\sqrt{49} \text { and } \sqrt{841} \text { is } 14.24}

<u>Solution:</u>

The Geometric mean between two numbers a and b is given as  Geometric mean = \bold{\sqrt{ab}}   --- eqn 1

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root for the numbers.

From question, given that two numbers are \sqrt{49} and \sqrt{841}

Hence we can say “a” = \sqrt{49} =7  

Similarly “b” = \sqrt{841} = 29  

We have to find the geometric mean between “7” and “29”

By using equation 1,  

Geometric mean between 7 and 29 = \sqrt{7 \times 29} = \sqrt{203} = 14.24

Hence the geometric mean between \sqrt{49} \text { and } \sqrt{841} \text { is } 14.24

8 0
3 years ago
If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. Find the first term and the 20th term.
Reil [10]

The first term is 2 and the 20th term is 1048576 .

<u>Step-by-step explanation:</u>

Here we have , If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. We need to Find the first term and the 20th term. Let's find out:

We know that Sum of a GP is :

⇒ S_n = \frac{a(r^n-1)}{r-1}

So ,Sum of first 12 terms is :

⇒ S_1_2 = \frac{a(2^{12}-1)}{2-1}

⇒ 8190=a(2^{12}-1)

⇒ \frac{8190}{4095}=a

⇒ a=2

Now , nth term of a GP is

⇒ a_n = ar^{n-1}

So , 20th term is :

⇒ a_2_0 = 2(2)^{20-1}

⇒ a_2_0 = (2)^{20}

⇒ a_2_0 = 1048576

Therefore , the first term is 2 and the 20th term is 1048576 .

8 0
3 years ago
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