Question

1. Describe the relationship between compound interest and exponential growth.

2. Describe how the account balance of a savings account earning simple interest is determined.

3. Explain the difference between a savings account earning simple interest and a savings account earning compound interest.

4. Which type of savings account would you open and why?


Please help.

Answer 1

Here is an example of compound interest
100 dollars invested for 3 years at 10% per year

amount after 3 years = 100(1 + 0.10)^3 = 133.10

Now suppose interest is paid every 6 months instead of yearly
that means that there will be 6 payments over the 3 years of 5%

amount after 3 years = 100(1 + 0.05)^6 = 134.01

so the more often the interest is paid the more you get

no if you g to the extreme and pay evry minute you can expect a lot more!

every second - a lot lot more

the limit of this will be when n (the number of times paid) approaches infinity

the exponential constant e = limit n--> infinity of (1 + 1/n)^n

its values is 2.71828 to 5 places of decimals

try working out (1 + 1/1000)^1000 on your calculator - yo'll get a value quite close to the constant e

Answer 2

Im still kinda confused....

Answer 3

maybe if I used fractions instead of decimals for compound interest

for 3 years annual payments
1 % = 1/100 = 0.01

we have ( 1 + 0.01)^3 -3 payments

payments every 6 months in terst will be half of 10 % = 0.10/2

we have (1 + 0.01/2)^(3*2)

for 4 payments a year we have
( 1 + 0.01/4)^(3*4)

for n years its (1 + 1/n)^n

now if n becomes a very big number the value of (1 + 1/n)^n will approach a limit which is about 2.71828 which is assigned the number e - the exponential constant

Answer 4

I just need a description, not really any examples.

Answer 5

so if any bank offer you exponential compound interest - grab it - you'll soon be very rich.

Answer 6

its hard to explain without giving examples

Answer 7

Haha thanks for the advice :) I know, its just I only need a description :/

Answer 8

They are the same. Compound interest is modeled and calculated by exponential growth.

Answer 9

tkhunny they are not the same.

Answer 10

I repeat, They are the same. Compound interest is modeled and calculated by exponential growth.