1) Ryan wants to invest for retirement. He has assets valuing $50,000 and is looking to invest for 15 years. Company A will grow his money with a 3.65% interest compounded quarterly. Company B will grow his money with a 3.75% interest. 1) Find the amount for each company and then 2) identify which company is the better choice.

Question

1) Ryan wants to invest for retirement. He has assets valuing $50,000 and is looking to invest for 15 years. Company A will grow his money with a 3.65% interest compounded quarterly. Company B will grow his money with a 3.75% interest. 1) Find the amount for each company and then 2) identify which company is the better choice.

2) Rachel purchased a new car for $37,500. The car is going to depreciate at a rate of 18% for the first 5 years. About how much will the car be worth after 42 months?

Answer 1

1) To find the amount for each company, we can use the compound interest formula:

For Company A:
A = P(1 + (r/n))^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (converted to decimal form)
n = number of times interest is compounded per year
t = number of years

For Company B:
A = P(1 + r)^t

Let's calculate the amounts for each company:

For Company A:
P = $50,000
r = 3.65% = 0.0365 (3.65% converted to decimal form)
n = 4 (quarterly compounding, 4 times per year)
t = 15 years

A = 50000(1 + (0.0365/4))^(4*15)
A = 50000(1 + 0.009125)^60
A ≈ $72,460.58

For Company B:
P = $50,000
r = 3.75% = 0.0375 (3.75% converted to decimal form)
t = 15 years

A = 50000(1 + 0.0375)^15
A ≈ $72,506.24

2) To calculate the approximate value of the car after 42 months, we need to apply the depreciation rate. We can use the formula:

P = P0 * (1 - r)^t
Where:
P = the final value
P0 = the initial value
r = depreciation rate (converted to decimal form)
t = time in years

Let's calculate the value of the car after 42 months:

P0 = $37,500
r = 18% = 0.18 (18% converted to decimal form)
t = 42 months / 12 months/year ≈ 3.5 years

P = 37500 * (1 - 0.18)^3.5
P ≈ $18,050.62

Therefore, the car will be worth approximately $18,050.62 after 42 months.

In conclusion, Company B is the better choice for Ryan's retirement investment, as it will yield a slightly higher final amount compared to Company A. As for Rachel's car, it will be worth approximately $18,050.62 after 42 months, considering an 18% depreciation rate over the first 5 years.