Question

You have $1,000 to invest for 8 years.  Banks offer you the following rates: 6% annual compounded APR, 5.8% semi-annual compounded APR, 5.5% continuously compounded APR.  Where do you want to invest and how much will you have?

Answer 1

Principal= $1000

Time= 8 years

Banks rate

1. option 1 = 6% annually compounded

2. option 2 =5.8% semi- annually compounded

3. option 3= 5.5% monthly compounded ( as continously compounded is mentioned)

Value in option 1: 1000*[1+(6/100)]^8

Value of option 2: 1000*[1+{(5.8*(6/12))/100}]^(8*2) { As semi annually means 6 months i.e, 1/2 of year so time is doubled and rate is halved )

Value of option 3: 1000*[1+{(5.5*(1/12))/100}]^8*12 { As monthly compounded so time *12 and rate/ 12 as there are 12 months in a year}

ON CALCULATING ,WE GET

1.Option 1 values to $ 1593.84

2. Option 2 values to $ 1579.95

3. Option 3 values to $1551.14

So, the best return is given by Option 1 i.e, 6% compounded annually.

ANSWER -Thus, i would like to invest in option 1 as it gives a return of $1593.84