Your dream is to buy a yacht currently valued at $300,000. you decide to put some money aside at the end of each month so you can buy your yacht without having to take out a loan. the bank guarantees an annual percentage rate of 5.1% as long as you have an account with them. if you decide to put aside $500 each month how long will it take you to buy this yacht if the current price stays the same? (round fractional year up).

It will take you 79 years to buy the yacht

Explanation:

The future amount of an investment can be calculated using the formula;

A=P(1+r)^n

where;

A=Future value of the investment

P=Initial deposit

r=annual interest rate

n=number of years of the investment

In our case;

A=300,000 since current price remains the same

P=(500×12)=6,000 yearly

r=5.1%=5.1/100=0.051

n=unknown

replacing;

300,000=6,000(1+0.051)^n

6,000(1.051)^n=300,000

1.051^n=300,000/6,000

1.051^n=50

ln 1.051^n=ln 50

n ln 1.051=ln 50

0.0497 n=3.912

n=3.192/0.0497

n=78.65 rounded up to 79 years

It will take you 79 years to buy the yacht

92.7 km

Explanation:

Since the magnetic field due to a solenoid is given by B = μ₀Ni/L where  μ₀ = permeability of free space = 4π × 10⁻⁷ H/m, N = number of turns of solenoid, L = length of cardboard tube = 58 cm = 0.58 m, , i = current in wire = 2.5 A and l = length of wire.

So, N = BL/μ₀i

Since B = 2.0 kG = 2.0 × 10³ G = 2.0 × 10³ × 10⁻⁴ T = 2.0 × 10⁻¹ T = 0.2 T

So, substituting the variables into the equation, we have

N = BL/μ₀i

N = 0.2 T × 0.58 m/(4π × 10⁻⁷ H/m × 2.5 A)

N = 1.16 Tm/(31.416 × 10⁻⁷ HA/m)

N = 0.0369 × 10⁷ turns

N = 0.0369 × 10⁷ turns

N = 3.69 × 10⁵ turns

length of wire l = NC where N = number of turns and C = circumference of tube = πD where D = diameter of tube = 8.0 cm = 0.08 m

So, l = NC

= NπD

= πND

= π × 3.69 × 10⁵ turns × 0.08 m

= 0.9274 × 10⁵ m = 9.274 × 10⁴ m

= 92.74 × 10³ m

= 92.74 km

≅ 92.7 km