Question

You are considering three alternative banks in which to open a savings account. The first bank offers you an annual rate r1, 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.

1) Suppose you were to save $500.0000 in the first bank. The interest rate is r1=8.0000%. Three years from now, you should have $

2) Suppose you were to save $500.0000 in the second bank. The interest rate is r2=5.0000%. Three years from now, you should have $

3) Suppose you were to save $500.0000 in the third bank. The interest rate is r3=3.0000%. Three years from now, you should have $

4) Let the interest rate in the first bank be r1=8.0000%, 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 r2=  

5) Let the interest rate in the third bank be r3=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 ?

Answer 1

1) Amount Saved = $500

r1 = 8%

N = 3 years

Formula with compounding effect of month = P [1 + r1 / (12 * 100)] ^{12 * n}

Thus it becomes = $500 [1 + 8 / (12 * 100)] ^{12 * 3} = $635.11

2) Amount Saved = $500

r2 = 8%

N = 3 years

Formula with compounding effect of daily = P [1 + r2 / (365 * 100)] ^{365 * n}

Assuming 365 days a year.

Thus it becomes = $500 [1 + 8 / (365 * 100)] ^{365 * 3} = $635.60

3) Amount Saved = $500

r3 = 8%

N = 3 years

Formula with compounding effect of month = P * e ^{r3 * n}

Thus it becomes = $500 * e ^{0.08 * 3}

= $635.62

4) Interest rate which will make you indifferent between first and second bank will give you the same Amount after 3 years of investment. Here r2 is giving you slightly more return than r1.

To make consumer indifferent, $635.11 = $500 [1 + r2 / (12 * 100)] ^{12 * 3}

r2 = 7.9995473%

This interest rate will make consumer indifferent between r1 and r2.

5) Interest rate which will make you indifferent between first and third bank will give you the same Amount after 3 years of investment. Here r3 is giving you slightly more return than r1.

To make consumer indifferent, $635.62 = $500 * e ^{r3 * 3}

r2 = 7.9995472%

This interest rate will make consumer indifferent between r1 and r3.