Student Question

$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?

Expert Answers

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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)


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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