Question

Assume one bank offers you a nominal annual interest rate of 6% compounded daily while another bank offers you continuous compounding at a 5.9% nominal annual rate. You decide to deposit $1,000 with each bank. Exactly two years later you withdraw your funds from both banks. What is the difference in your withdrawal amounts between the two banks?

Answer 1

Answer:

difference in withdrawal amounts between the two banks is $2.24

Explanation:

given data

interest rate = 6% compounded daily

continuous compounding rate = 5.9% nominal annual rate

deposit = $1,000

to find out

What is the difference in your withdrawal amounts between the two banks

solution

we find first future value by compounded daily that is

future value = $P ( 1 + \frac{r}{365} )^{365*t}$    ...........1

here P is deposit amount and r is rate and t is time i.e 2 year

so

future value = $1000( 1 + \frac{0.06}{365} )^{365*2}$

future value =  $1127.48    ...............a

and

future value by continuous compounding that is

future value = $P(e)^{r*t}$    ...........2

here P is deposit amount and r is rate and t is time i.e 2 year

so

future value = $1000(e)^{0.059*2}$  

future value = 1125.24      ...................b

so

difference in future value is = a - b

difference in future value is = 1127.48 - 1125.24

difference in withdrawal amounts between the two banks is $2.24