Question

In: Advanced Math

karla has opened an IRA in which she deposits $250 each month that earns 3.5% interest...

karla has opened an IRA in which she deposits $250 each month that earns 3.5% interest compounded monthly

how much money will she have in the account after 25 years?

how much total money will she put into the account?

how much total interest will she earn?

Expert Solution

Let us assume the monthly deposits are made at end of the every month then it is knowing as ordinary annuity

We can use the formula for finding the future value as below

A = p x [ ( 1 + (r/n) )^nt-1 ] / ( r/n )

Here A = future value = $?

p = Cash flow per period = $250

r = rate of interest = 3.5% = 3.5/100 = 0.035

n = compounding frequency is monthly so n= 12

t = Number of years = 25

A = 250 x [ ( 1 + (0.035/12 ))¹²⁽²⁵⁾ – 1 ] / (0.035/12)]

A = 250 x [ ( 1 + (0.0029167 ))³⁰⁰ – 1 ] / (0.0029167)]

A = 250 x [ ( 1.0029167 ))³⁰⁰ – 1 ] / (0.0029167)]

A = 250 x [ 2.395846 – 1 ] / (0.0029167)]

A = 250 x [ 1.395846] / (0.0029167)]

A = 250 x [ 478.57]

A = 119642.5

So the accumulated amount in the account after 25 years = $119642.5

b) the total money put into the account = 25 x 12 x 250 = $75000

c ) total interest earned = accumulated value – total money deposited

total interest earned = 119642.5 – 75000 = $44642.5

Colby Messinger answered 6 months ago

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