Question

You have $10,000dollars and want to invest them in the best possible option.
• Bank A offers to pay 4.1% compounded quarterly
• Bank B offers to pay 4% interest, compounded monthly
• Bank C offers to pay 4.1% compounded semesterly
Additionally, petrol/ transport costs to deposit and to collect the money are:
• Bank A is online (assume free)
• Bank B is $15 per trip
• Bank C $12 per trip.
If you are planning to leave the money in the bank for three years, what option is the best ?

Answer 1

Answer on Question #80347 - Economics / Economics of Enterprise

QUESTION: You have $10,000 dollars and want to invest them in the best possible option.

- Bank A offers to pay 4.1% compounded quarterly

- Bank B offers to pay 4% interest, compounded monthly

- Bank C offers to pay 4.1% compounded semesterly

Additionally, petrol/ transport costs to deposit and to collect the money are:

- Bank A is online (assume free)

- Bank B is $15 per trip

- Bank C $12 per trip.

If you are planning to leave the money in the bank for three years, what option is the best?

ANSWER.

The formula for annual compound interest, including principal sum, is:

$$A = P (1 + r / n)^{(nt)}$$

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

1. For bank A: compounded quarterly using the formulae you get:

$$A = \$10,000(1+0.041/3)^{3+3}$$ $$A = \$11,299.43$$

2. For bank B... compounded monthly

$$A = \$10,000(1+0.04/12)^{12+3}$$ $$A = \$11,272.72$$

3. For bank C... compounded semesterly

A = $10,000 (1 + 0.041/6)^{6+3}$

A = $11,304.11

Petrol/ transport costs to deposit and to collect the money

Bank A is free therefore no cost.

Total = $11,299.43

Bank B is $15 per trip (2 trips, deposit and withdraw)

therefore $11,272.72 - ($15*2) = $11,242.72

Bank C $12 per trip (2 trips, deposit and withdraw)

therefore $11,304.11 - ($12*2) = $11,280.11

The best option is bank A which is $11,299.43

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