Question

A. Suppose you were to save $500.0000 in the first bank. The interest rate is ?1=9.0000. Three years from now, you should have $ ______

You are considering three alternative banks in which to open a savings account. The first bank offers you an annual rate ri, and the interest is paid monthly. The second bank offers a rate r2, and the interest is paid daily. The third bank offers a rate r3, and it offers continuous compounding. Give all answers to four decimal places.

B. Suppose you were to save $500.0000 in the second bank. The interest rate is ?2=6.0000. Three years from now, you should have $ ______

C. Suppose you were to save $500.0000 in the third bank. The interest rate is ?3=3.0000. Three years from now, you should have $ ______

D. Let the interest rate in the first bank be ?1=9.0000, and you are considering saving your money for 3 years. The interest rate from the second bank that would make you indifferent between the first and second bank is ?2= ______%

E. Let the interest rate in the third bank be ?3=3.0000, and you are considering saving your money for 3 years. The interest rate from the first bank that would make you indifferent between the first and third bank is ?1= ______%

Answer 1

Ans A-

Answer:

A = $635.00

(I = A - P = $135.00)

Equation:
A = P(1 + rt)

Calculation:
First, converting R percent to r a decimal
r = R/100 = 9%/100 = 0.09 per year.

Putting time into years for simplicity,
36 months / 12 months/year = 3 years.

Solving our equation:
A = 500(1 + (0.09 × 3)) = 635
A = $635.00

The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 9% per year for 3 years (36 months) is $635.00.

Answer:B

A = $590.00

(I = A - P = $90.00)

Equation:
A = P(1 + rt)

Calculation:
First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year.

Putting time into years for simplicity,
1095 days / 365 days/year = 3 years.

Solving our equation:
A = 500(1 + (0.06 × 3)) = 590
A = $590.00

The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 6% per year for 3 years (1095 days) is $590.00.

Ans C

A = $ 547.09

A = P + I where
P (principal) = $ 500.00
I (interest) = $ 47.09

Ans D

Total interest accrued from Bank 1 = $135 $(635-500)

Total interest accrued from Bank 2 = $ 90 $(590-500)

Excessive total percentage- = $135-$90=$45

In % - 45/90*100= 50% - Interest will be 50% extra as compared to bank 1

Ans E

As per calculation for Ans C with rate of interest of 3% for Bank 3 the total amount will be $ 547.09 in which $47.09 is the interest amount

Total amount in the first bank after 3 year- $ 590 I.e, $90 as interest

Excess interest- $90-47.09= $42.91

Percentage difference

42.91/90*100= $47.67% It means excessive interest payable in bank 1 is $47.67%