Ask question

Ask question

All categories

2 years ago

11

Kathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a ho

me for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years?
a) About 12%
b) About 13%
c) About 9%
d) About 10%

1 answer:

olga_2 [115]2 years ago

6 0

Answer:

a) About 12%

Step-by-step explanation:

We need to find the interest rate required to achieve her goal, so we will need to use the interest-compound formula:

$FV=PV(1+i)^{n}$

Where:

PV= Present Value

i= interest rate

FV= Future Value

n= number of periods

replacing the data provided:

$150.000=50.000(1+i)^{10}$

solving for i:

first, divide both sides by 50.000 to simplify the equation:

$3=(1+i)^{10}$

Take $10^{th}$ roots of both sides:

$1+i=$ ± $\sqrt[10]{3}$

solve for i:

$i=$ ± $\sqrt[10]{3} -1$

We get two answers, but we look for a coherent value. So we take the positive one:

$i=11.6123174$ ≈12

You might be interested in

casey bought sandwiches and a bag of chips. Each sandwich cost three times as much as bag of chips. She bought 5 sandwiches for

balandron [24]

Answer:

4

Step-by-step explanation:

If sandwiches are 6 dollars each, then chips are 3 dollars, she only bought 5 sandwiches for 6 each for 30 dollars(5*6=30).So, she has 12 dollars left to spend since she spent 42 dollars. And 4 *3=12so she only bought 4 bags of chips.

3 0

2 years ago

Read 2 more answers

Madison randomly surveyed 50 students at her high school about their favorite color, and 18 students chose blue. Madison conclud

Aleks04 [339]

Should be A, if not then prolly B

4 0

2 years ago

Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant

Viktor [21]

Answer:

Therefore $k= \frac{ln2 }{18}$ , A=184

Step-by-step explanation:

Given function is

$T(t)=230 -e^{-kt}$

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

$138=230 -Ae^{-k\times 18}$

$\Rightarrow -Ae^{-18k}=138-230$

$\Rightarrow Ae^{-18k}=92$ .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

$184=230-Ae^{-k\times 36}$

$\Rightarrow Ae^{-36k}=230-184$

$\Rightarrow Ae^{-36k}=46$ .......(2)

Dividing (2) by (1)

$\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}$

$\Rightarrow e^{-18k}=\frac{46}{92}$

Taking ln both sides

$ln e^{-18k}=ln\frac{46}{92}$

$\Rightarrow -18k =ln (\frac12)$

$\Rightarrow -18k= ln1-ln2$

$\Rightarrow k= \frac{ln2 }{18}$

Putting the value k in equation (1)

$Ae^{-18\frac{ln2}{18}}=92$

$\Rightarrow A e^{ln2^{-1}}=92$

$\Rightarrow A.2^{-1}=92$

$\Rightarrow \frac{A}{2}=92$

$\Rightarrow A= 92 \times 2$

⇒A= 184.

Therefore $k= \frac{ln2 }{18}$ , A=184

7 0

2 years ago

Shari walks 5 blocks to school each morning.The walk takes 10 minutes

olga2289 [7]

Answer:
If she walks 5 blocks and it takes 10 minutes each block takes 2 minutes to walk.

10
— = 2 So 2 minutes per block
5

4 0

2 years ago

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as

Rzqust [24]

Answer:

109.9 ft

Step-by-step explanation:

The length of an arc that is 1/4 of a circle of radius 70 ft is ...

s = rθ

s = (70 ft)(π/2) = 35π ft ≈ 109.9557 ft

The best answer choice appears to be 109.9 feet.

4 0

2 years ago

Read 2 more answers