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$100 dollars is deposited each month for 20 years into an account paying 6% interest,...

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sss2855 | eNotes Newbie

Posted October 28, 2013 at 8:52 PM via web

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$100 dollars is deposited each month for 20 years into an account paying 6% interest, compounded monthly. No more deposits are made but the account still earns interest. How much is in the account when the person retires 25 years after the last deposit?

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted October 29, 2013 at 5:16 AM (Answer #1)

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To calculate the amount after the first 20 years during which time $100 is deposited monthly use the formula:

`F=(x[(1+i)^n-1])/i` where F= the total after 20 years, x=$100pm, i=6% compounded monthly=`0.06/12=0.005` and n=20 years x12 months (compounded monthly)=240.

`therefore F=(100[(1+0.005)^240-1])/0.005`

`therefore F=$46204.08952` As the calculations will continue, do not round off at this stage. 

Now calculate the amount saved after a further 25 years. As there are no deposits , use the formula:

`F=P(1+i)^n` where P=$46 204.08952 and n=25 x12=300 i=0.005 as we are still compounding monthly and F will be the final total.

`therefore F=46204.08952(1+0.005)^300`  

`therefore F=$206299.86` (rounded off)

Ans:

After 20 years of monthly deposits of $100 and another 25 years of continuing compound interest on the accumulated amount, the total amount saved will be $206 299.86.

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