Question

A friend wants to deposit $2000 into a savings account. She goes to two banks and is offered competing interest rates for the account. Bank 1 has a 10% interest rate, and compounds once annually. Bank 2 has an 9% interest rate, but compounds monthly. Use the following annually compounded interest formula,

A=P(1+r)^t

where A is the accumulated amount, P is the principal amount deposited, r is the annual interest rate (as a decimal) and t is the number of years. For accounts that compound more frequently than once annually, you must use

A=P(1+r/m)^tm

where m is the number of times the account compounds per year. Use fprintf to create a table for all account balances for the first five years for each account so that your friend can compare and decide which one to select. (i.e. year, compound monthly into annunal amount, annual amount).

Answer 1

Solution:

The values provided in the question are are follows:

Initial Deposit Amount = $ 2000

Interest Rate in Bank 1 = 10% (Compounds once annually)

Interest Rate in Bank 2 = 9 % (Compounds monthly, ie., 12 times per year)

Number of years = 5 years

Formula for Annually Compounded Interest,

A = P(1+r/m)^tm

A - Accumulated Amount

P - Principal Amount

r - Annual Interest rate

t - Number of years

m - Number of times the account compounds per year

As per formula, Annual compounded interest from Bank 1 is

A = 2000 * (1 + (0.1/1))^5*1

A = 2000 * (1.1)^5

A = 2000 * 1.6105

A = 3221.02

Hence, the expected return from Bank 1 in 5 years is $ 3221.02

As per formula, Annual compounded interest from Bank 2 is

A = 2000 * (1 + (0.09/12))^5 * 12

A = 2000 * (1 + 0.0075)^60

A = 2000 * 1.5657

A = 3131.36

Hence, the expected return from Bank 2 in 5 years is $ 3131.36

A tables for all account balances for the first five years to compare and decide which one to select,

Table - 1 for Bank 1

Bank 1
Year	Interest Amount	Annual Amount
1	200	2200
2	420	2420
3	662	2662
4	928.2	2928.2
5	1221.02	3221.02

Table - 2 for Bank 2

Bank 2
Year	Interest Amount	Annual Amount
1	187.61	2187.61
2	392.83	2392.83
3	617.29	2617.29
4	862.81	2862.81
5	1131.36	3131.36