Choice 1: Payments of $ 2600 now, $ 3200 a year from now, and $ 3880 two years from now.
Choice 2: Three yearly payments of $ 3200 starting now.
Modification: Interest is compounded continuously instead of annually.
(a) If the interest rate on savings were 4.86 %, which would you prefer?
(Type in 1 for Choice 1, or 2 for Choice 2.)
(b) What is the interest rate that would make both choices equally lucrative?
2 answers
a.) choice 1
Assuming choices are payment options, i.e. we will be paying the said amounts.
Total amount of payment for each choice is $9600.
Assuming we have $9600 in the bank, we calculate what would we have accumulated in interest at the end of two years.
Choice 1:
3800 for 2 years +
3200 for 1 year.
Interest at annual rate 4.86%
=3800*1.0486²-3800+3200*0.0486
=533.86
Choice 2:
3200 for 2 years + 3200 for 1 year
Interest at continuous rate of 4.86%
=3200(e^(.0486*2))-3200+3200(e^(.0486))-3200
=486.02
So the first choice is more profitable.
Total amount of payment for each choice is $9600.
Assuming we have $9600 in the bank, we calculate what would we have accumulated in interest at the end of two years.
Choice 1:
3800 for 2 years +
3200 for 1 year.
Interest at annual rate 4.86%
=3800*1.0486²-3800+3200*0.0486
=533.86
Choice 2:
3200 for 2 years + 3200 for 1 year
Interest at continuous rate of 4.86%
=3200(e^(.0486*2))-3200+3200(e^(.0486))-3200
=486.02
So the first choice is more profitable.
0 answers