# I'm not sure how to work out this problem...?

My teacher wants to know if it's better to invest \$10,000 at birth at 8% compounded daily (Funding Supplied by government program) or Contribute to Social Security for retirement as we do now?

He said to calculate how much will the 10,000 accumulate to in 65 years...

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• 9 years ago

Are you sure he said 8% compounded DAILY ??!!?? That would become an astronomically large amount over 65 years. (Actually, it would become a HUGE number in a lot less than 65 years.) I don't even think the calculator on my computer could display such a large number.

But, I'll see . . .

Here's the formula :

A = P * [ 1 + (r/n) ]^(nt)

P = principal amount (the initial amount you borrow or deposit)

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n = number of times the interest is compounded per year

In this problem (as stated with DAILY compound interest) ,

P = 10000

r = 29.2 . . . . . . . . . . [ ** See note below ** ]

t = 65

n = 365

A = 10000 * [ 1 + (29.2 / 365) ]^ (365 * 65)

= 10000 * [ 1 + 0.08 ] ^ (23,725)

= 10000 * [ 1.08 ] ^ (23,725)

and . . .

the calculator explodes, as I predicted !

[ ** Note : This is where the compounded DAILY comes into play.

8% interest per day = (0.08 x 365) = 29.2 , or an interest rate of 2,920% per year !

This is not realistic. Forgive me if I think of the word loony ** ]

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OK. Let's try this again in case he meant 8% compounded YEARLY.

(much more realistic)

In this new scenario,

P = 10000

r = 0.08

t = 65

n = 1

A = 10000 * [ 1 + (0.08 / 1) ]^ (1 * 65)

= 10000 * [ 1.08 ]^ (65)

= 10000 * 148.779846621

= 1,487,798.47 [rounded]

Now that result is more realistic. \$10,000 invested at birth with interest compounded at 8% per year amounts to about 1.5 million in 65 years, which I am confident far outweighs any current Social Security system plan.