Question

please show work!!

You are about to deposit $671 into one of the following savings accounts to be left on deposit for 25 years. Each bank offers an account with a different interest rate and compounding period. Assuming you want to maximize your wealth, how much money would be in the bank account that offers the best effective rate of return after 25 years? BANK A: 9.5 percent rate compounded semi-annually BANK B: 9.4 percent rate compounded monthly BANK C: 9.3 percent rate compounded daily BANK D: 9.2 percent rate compounded continuously (Enter the dollar amount only - do NOT enter the bank letter. Round your answer to 2 decimal places and record your answer without a dollar sign and without commas).

Answer 1

1]

Bank A

Future value = present value * (1 + r)ⁿ,

where r = periodic interest rate

n = number of periods.

In this case, r = 4.75% (Since there are 2 semiannual periods in a year, semiannual rate = annual rate / 2 = 9.5% / 2 = 4.75%).

n = 50 (number of semiannual periods = number of years * 2 = 25 * 2 = 50).

Future value = $671 * (1 + 4.75%)⁵⁰

Future value = $6,830.05.

Bank B

Future value = present value * (1 + r)ⁿ,

where r = periodic interest rate

n = number of periods.

In this case, r = 0.7833% (Since there are 12 months in a year, monthly rate = annual rate / 12 = 9.4% / 12 = 0.7833%).

n = 300 (number of months = number of years * 12 = 25 * 12 = 300).

Future value = $671 * (1 + 0.7833%)³⁰⁰

Future value = $6,971.69.

Bank C

Future value = present value * (1 + r)ⁿ,

where r = periodic interest rate

n = number of periods.

In this case, r = 9.3%/365 (Since there are 365 days in a year, daily rate = annual rate / 365 = 9.3% / 365).

n = 9125 (number of days = number of years * 365 = 25 * 365 = 9125).

Future value = $671 * (1 + (9.3%/365))⁹¹²⁵

Future value = $6,860.07.

Bank D

Future value = present value * e^rt,

where r = rate of interest, and t = time in years.

Future value = $671 * e^0.092*25

Future value = $6,692.68.

Bank B offers the highest future value after 25 years. The money in account will be $6,971.69.