Finite Math Compound Interest 17 February / 10

Transcript

1 Copound Interest Finite Math 17 February 2017 Finite Math Copound Interest 17 February / 10

2

3

4 A =

5 A = future value,

6 A = future value, P =

7 A = future value, P = principal,

8 A = future value, P = principal, r =

9 A = future value, P = principal, r = annual noinal interest rate,

10 A = future value, P = principal, r = annual noinal interest rate, =

11 A = future value, P = principal, r = annual noinal interest rate, = nuber of ties per year interest is copounded,

12 A = future value, P = principal, r = annual noinal interest rate, = nuber of ties per year interest is copounded, n =

13 A = future value, P = principal, r = annual noinal interest rate, = nuber of ties per year interest is copounded, n = total nuber of copoundings.

14 A = future value, P = principal, r = annual noinal interest rate, = nuber of ties per year interest is copounded, n = total nuber of copoundings. Continuously Copounded Interest

15 A = future value, P = principal, r = annual noinal interest rate, = nuber of ties per year interest is copounded, n = total nuber of copoundings. Continuously Copounded Interest e rt

16 A = future value, P = principal, r = annual noinal interest rate, = nuber of ties per year interest is copounded, n = total nuber of copoundings. Continuously Copounded Interest e rt A, P, and r are the sae as above and t is tie easured in years.

17 Continuous Copound Interest Exaple If $1, 000 is invested at 6% interest copounded continuously, what is the value of the investent after 8 years? Round answers to the nearest cent. Finite Math Copound Interest 17 February / 10

18 Now You Try It! Exaple If $2, 000 is invested at 7% copounded a) daily, b) continuously, what is the aount after 5 years? How uch interest is accrued in each case? Round answers to the nearest cent. Assue 365 days in a year.) Finite Math Copound Interest 17 February / 10

19 Now You Try It! Exaple If $2, 000 is invested at 7% copounded a) daily, b) continuously, what is the aount after 5 years? How uch interest is accrued in each case? Round answers to the nearest cent. Assue 365 days in a year.) Solution a) $ with $ in interest. b) $ with $ in interest. Finite Math Copound Interest 17 February / 10

20 Copound Interest As before, we can use these copound interest odels to figure out how uch we should invest now to achieve a desired future value. Finite Math Copound Interest 17 February / 10

21 Copound Interest As before, we can use these copound interest odels to figure out how uch we should invest now to achieve a desired future value. Exaple New parents are looking at a college savings account which gives 8% interest. If they are looking to have $80, 000 when their child is ready to go to college in 17 years, how uch should they invest now if interest is copounded a) seiannually, b) continuously? Round answers to the nearest cent. Finite Math Copound Interest 17 February / 10

22 Now You Try It! Exaple You are looking at a retireent account which pays 2% interest. If you are looking to have $1, 000, 000 in the account by the tie you retire in 50 years how uch should you invest now if interest is copounded a) quarterly, b) continuously? Round answers to the nearest cent. Finite Math Copound Interest 17 February / 10

23 Now You Try It! Exaple You are looking at a retireent account which pays 2% interest. If you are looking to have $1, 000, 000 in the account by the tie you retire in 50 years how uch should you invest now if interest is copounded a) quarterly, b) continuously? Round answers to the nearest cent. Solution a) $368, b) $367, Finite Math Copound Interest 17 February / 10

24 Copound Interest Exaple How long will it take $10, 000 to grow to $25, 000 if it is invested at 8% copounded quarterly? Finite Math Copound Interest 17 February / 10

25 Now You Try It! Exaple How long will it take oney to triple if it is invested at a) 5% copounded daily? b) 6% copounded continuously? Finite Math Copound Interest 17 February / 10

26 Now You Try It! Exaple How long will it take oney to triple if it is invested at a) 5% copounded daily? b) 6% copounded continuously? Solution a) 8, 021 days about years) b) years Finite Math Copound Interest 17 February / 10