Please help with this

Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.

anzhelika [568]

Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
$V_{0} =(1+ i_{a} ) ^{1}$
Where
$V_{0}$ = initial investment.
$i_{a}$ = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
$V_{0} =(1+ i_{q} ) ^{4}$
Where
$V_{0}$ = initial investment.
$i_{q}$ = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
$(1+ i_{a} )=(1+ i_{q} ) ^{4}$
Notice that we are not using the initial investment $V_{0}$ since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
$(1+0.07)=(1+ i_{q} ) ^{4}$
$1.07=(1+ i_{q} ) ^{4}$
$\sqrt[4]{1.07} =1+ i_{q}$
$i_{q} = \sqrt[4]{1.07} -1$
$i_{q} =0.017$
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.

6 0

3 years ago

The dot plot shows how many swimmers are in each line at a waterpark: Dot plot titled Swimmers in Line and labeled Number of Swi

nasty-shy [4]

The answer is median, because the data is skewed and there is an outlier.

3 0

3 years ago

Read 2 more answers

HELP ME PLLLLZ dis is PEMDAS

hram777 [196]

Answer:

Give Branliest PLz

Answer is 15

Step-by-step explanation:

Half of 40 is 20 cause 40/2=20

Five less than 20 is 20-5 which= 15

So ur answer is 15

6 0

3 years ago

Read 2 more answers

A small resort is situated on an island that lies exactly 3 miles from P, the nearest point to the island along a perfectly stra

Artemon [7]

Answer:

The distance from the shoreline from P the pipe from the island will reach land in order to minimize the total construction cost is 0 m, or the pipe should be routed to the point P

Step-by-step explanation:

We note that, cost to lay pipe in water = 2.3 × cost to lay pipe on land

Distance of the small resort on the island from point p on the shoreline = 3 miles

Location of the closest source of fresh water is 10 miles along the shoreline from p

∴ The small resort, the point p and the closest source of the fresh water on the shoreline together form a right triangle with sides

Height = 3 miles

Base = 10 miles and

Hypotenuse = $\sqrt{3^2 + 10 ^2} = \sqrt{109} = 10.44 \, m$

To find the cost of laying the pipeline by the various route, we multiply the water routes by 2.3 and the land routes by 1 and we get

Costs:

Height = Water route = 2.3 × 3 miles = 6.9

Base = Land route = 1 × 10 miles = 10

Hypotenuse = Water route = 2.3 × 10.44 miles = 24.012

Therefore, the two routes are either

10 miles to point p and 3 miles across the water to the resort with a cost = 10 + 6.9 = 16.9 or

Directly to the small resort through 10.44 miles across the water with cost = 24.012

Therefore, to minimize cost, the pipe should come from the resort to P from there to the fresh water source.

That is the distance from the shoreline from P the pipe from the island will reach land in order to minimize the total construction cost = 0 m.

7 0

3 years ago

What's the square root of 120

gladu [14]

The square root of 120 rounded to the nearest hundredth would be 10.95.

3 0

3 years ago