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3 years ago

8

how much must you deposit in an account that pays 8% annual interest compounded monthly to have a balance of $1,000 after one ye

ar

1 answer:

strojnjashka [21]3 years ago

5 0

Answer:

$\$923.36$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=1\ year\\ A=\$1,000\\ r=0.08\\n=12$

substitute in the formula above and solve for P

$\$1,000=P(1+\frac{0.08}{12})^{12*1}$

$P=\$1,000/(1+\frac{0.08}{12})^{12*1}=\$923.36$

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In ΔUVW, w = 9 cm, v = 2.2 cm and ∠V=136°. Find all possible values of ∠W, to the nearest 10th of a degree.

Alja [10]

Complete Question

In ΔUVW, w = 9 cm, v = 22 cm and ∠V=136°. Find all possible values of ∠W, to the nearest 10th of a degree.

Answer:

16.5°

Step-by-step explanation:

In ΔUVW, w = 9 cm, v = 22 cm and ∠V=136°. Find all possible values of ∠W, to the nearest 10th of a degree.

We solve using Sine rule formula

a/sin A = b/sin B

We are solving for angle W

∠V=136°

Hence:

22 /sin 136 = 9 /sin W

Cross Multiply

22 × sin W = sin 136 × 9

sin W = sin 136 × 9/22

W = arc sin [sin 136 × 9/2.2]

W = 16.50975°

W = 16.5°

3 0

3 years ago

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

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UNO [17]

Your answer should be organize, correct me if I’m wrong !

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