Question

With all of the extra profit being made at Mr. Alfredo’s Amazing Pasta Sauce Company, a decision has to be made on how to invest it.

Bank A and Bank B Uses Simple Interest: ? = ??? I = Interest earned P = Principal r = Interest rate t = Time (years)

Bank C Uses Compound Interest: ? = ?(1 + ?)5 A = Amount you end with P = Principal Bank A offers a 3% interest rate on the first $30,000 invested and then a 4.5% interest rate on any money invested over $30,000. Bank B offers a 4% interest rate on all money invested.

1) If $50,000 is invested, which bank would give you a better return on investment after 10 years?

2) How much money needs to be invested for Bank A to be a better choice than Bank B? Answer this with an inequality.

3) Bank C offers a 3% interest rate. If $60,000 is now invested, will Bank C be a better option than Bank A and Bank B after 10 years?

Answer 1

Answer:

Data given:

Bank A and Bank B uses simple interest given by -

1 = Prt

where I - Interest earned, P - Principal, r - Interest rate, t - Time (years)

Bank C uses compound interest given by -

A= P(1+r)

where A - Total amount after t years, P - Principal, r - Interest rate, t - Time (years)

Bank A offers 3% interest rate on the first $30000 invested and then a 4.5% interest rate on any money invested over $30000.

Bank B offers a 4% interest rate on all money invested.

(a). Invested amount or principal amount, P = $50000

Time period, t = 10 years

Now, we can calculate the interest earned at Bank A and Bank B using the simple interest formula as -

Bank A: 14 = Pxrxt

  

4.5 = 30000 x P x 10+ 20000 x 100 x 10

= 9000+ 9000

$Bank \ B : I_{B} = P \times r \times t$

$= 50000 \times \frac{4}{100} \times 10$   

.

Thus, Bank B offers a better return on the investment.

(b). Now, in order to find the principal amount P that need to be invested in Bank A and Bank B such that Bank A offers better return, we can the write the inequality as -

Let the time period for the investment be "t".

$30000 \times \frac{3}{100} \times t + (P-30000) \times \frac{4.5}{100} \times t > P \times \frac{4}{100} \times t$ ( Since P > 30000 for Bank A to offer better return )

$30000 \times \frac{3}{100} + (P-30000) \times \frac{4.5}{100} > P \times \frac{4}{100}$

Thus, a principal amount greater than $90000 needs to be invested for Bank A to offer better return than Bank B.

(c). Invested amount or principal amount, P = $60000

Time period, t = 10 years

Rate of interest offered by Bank C = 3%

Now, we can calculate the interest earned at Bank A and Bank B using the simple interest formula as -

Bank A: 14 = Pxrxt

$= 30000 \times \frac{3}{100} \times 10 + 30000 \times \frac{4.5}{100} \times 10$   

$Bank \ B : I_{B} = P \times r \times t$

$= 60000 \times \frac{4}{100} \times 10$   

.

Now, we can calculate the interest earned at Bank C using the compound interest formula as -

1. Interest earned at Bank C = 80634.98 - 60000

Thus, Bank C is not a better option for this investment.