How much interest does 40000 generate in a savings account?

Answer 1

There are four factors which determine the answer to "how much interest does 40,000 generate in a savings account". Namely,

r - The rate of return the savings account pays

k - The rate of compounding

t - The length of time the money resides in the account

P - the principal involved, in this case, $40,000

The formula for the balance, B, is generally expressed as a function of time, t

B(t) = P [ 1 + (r/k) ] kt

If the rate is 5%, compounded monthly for one year then the formula becomes

B(1) = 40000 [ 1 + (0.05/12) ] ) 12x1

B(1) = 40000 [ 1 + 0.0041666 ] 12

B(1) = 40000 [ 1.0041666] 12

B(1) = 40000 ( 1.0511619 )

B(1) = 42,046.48

The amount of interest earned for that time frame is the difference between the final balance and the principal you started with or (42046.48 - 40000) which equals 2,046.48

Alternatively, you can use the basic formula for interest which is

i = Prt

which gives us

i = 40000 x 0.05 x 1

i = 2,000

however, with this simple interest formula the effects of compounding are neglected.

It is also possible for interest to be compounded continuously in which case we add the value e (e ~ 2.71828183) into our original equation or,

B(t) = Pert

B(t) = 40000e(0.05x1)

B(t) = 40000 x 1.05127

B(t) = 42050.84

in which case our interest earned is 42050.84 - 40000 or $2,050.84. This is $4.36 more than if our money were only compounded monthly.