Please show me how you answer the question step by step You

Please show me how you answer the question step by step.

You are saving to buy a new $200,000 Ferrari. You have $100,000 today that can be invested at your bank. The bank pays 5 percent annual interest. How long will it be before you have enough to buy the car?

–with annual compounding

–with quarterly compounding

Solution

Answer a.

Desired Sum = $200,000
Amount Invested = $100,000
Annual Interest Rate = 5%

Let it will take ‘n’ years to accumulate desired sum

Amount Invested * (1 + Interest Rate)^Period = Desired Sum
$100,000 * (1 + 0.05)^n = $200,000
1.05^n = 2
n * ln(1.05) = ln(2)
n = 14.21

So, it will take 14.21 years to buy the car.

Answer b.

Desired Sum = $200,000
Amount Invested = $100,000
Annual Interest Rate = 5%
Quarterly Interest Rate = 1.25%

Let it will take ‘n’ quarters to accumulate desired sum

Amount Invested * (1 + Interest Rate)^Period = Desired Sum
$100,000 * (1 + 0.0125)^n = $200,000
1.0125^n = 2
n * ln(1.0125) = ln(2)
n = 55.80

Number of quarters = 55.80
Number of years = 55.80 / 4
Number of years = 13.95

So, it will take 13.95 years to buy the car.