Please help with this kenken puzzle

2. Harry just deposited $1500 into a savings account giving 6% interest compounded quarterly.a) How much will be in the account

Studentka2010 [4]

The formula for compound interest is:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ Final amount} \\ r=\text{ Interest rate} \\ n=\text{ Number of times interest applied per period} \\ t=\text{ Number of time period elapsed} \\ P=\text{ Intial principal balance} \end{gathered}$

Given data:

$\begin{gathered} P=\text{ \$1500} \\ r=6\text{ \%}=0.06 \\ n=4\text{ times (compounded quarterly)} \end{gathered}$

a. After ten years, that is t = 10 years, the amount in the account will be

$\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times10} \\ A=\text{ }1500(1+0.015)^{40} \\ A=\text{ }1500(1.015)^{40} \\ A=\text{ \$2721.03} \end{gathered}$

b. After twenty years, that is t = 20 years, the amount in the account will be:

$\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times20} \\ A=1500(1.015)^{4\times20} \\ A=1500(1.015)^{80} \\ A=\text{ \$}4935.99 \end{gathered}$

c. The time it takes for Harry's initial account value to double will be:

$\begin{gathered} A=2\text{ x initial value = 2 }\times\text{ \$1500 = \$3000} \\ 3000=1500(1.015)^{4t} \\ (1.015)^{4t}=\frac{3000}{1500} \\ (1.015)^{4t}=2 \\ \text{ Find the logarithm of both sides} \\ \ln (1.015)^{4t}=\ln 2 \\ 4t=\frac{\ln 2}{\ln 1.015} \\ 4t=46.56 \\ t=\frac{46.56}{4}=11.64 \end{gathered}$

Therefore, the time it takes Harry's initial account to double is approximately 11 years

8 0

1 year ago

How do you solve this ?

Inga [223]

2.) y = x - 12

3.) 2x + 6

6 0

3 years ago

The length of a quarter is 0.953 inch. round the length of a quarter to the nearest tenth of an inch

liraira [26]

Answer:

1 inch

Step-by-step explanation:

The 9 is in the tenths place so you look to the hundredths place and if the number is greater than or equal to 5 then the 9 can round up.

The hundredths place is 5 so the 9 rounds up and since it can not round up in the tenths place you put the rounding in the front so the answer is 1 inch.

6 0

3 years ago

Help!!!! I really need help with this I don’t understand it!!!

Temka [501]

9514 1404 393

Answer:

y = 5

Step-by-step explanation:

There are a number of ways to get there, but the short of it is that a horizontal line has the equation ...

y = constant

The constant value must be chosen to match the y-value of points on the line. Here, that is 5. The equation of the line is ...

y = 5

_____

<em>Another way</em>

You can write the equation in slope-intercept form if you know the slope and the y-intercept. The line crosses the y-axis at y = 5, so that is the value of the y-intercept.

The "rise" between the two points is 5 -5 = 0. The "run" between the two points is 5-0 = 5, so the slope is ...

m = rise/run = 0/5 = 0

Then the slope-intercept equation is ...

y = mx + b . . . . . where m is the slope and b is the y-intercept

y = 0x +5

Simplifying, we get ...

y = 5

6 0

3 years ago

Can somebody help me

saveliy_v [14]

Answer:

Y=5

You must first divide b (-10) by two and square it to know what you need to make a perfect square (25). You must then add or subtract the amount to make C (-13) into that number (add 38). Don't forget to do it on the other side too! (3 becomes 41) You then factor the left side. ((Y-5)^2=41) The result is your answer. (Y=5)

6 0

3 years ago