John's unconventional financial situation v2
(Don't use graphing) (I think this might be more simple then v1, eh...)
John has created 2 new bank accounts: one with a compound interest growth of 2% , and one with a simple interest growth of 3% (both p.a)
If John deposits $20 into both banks how old will John be (in years) (if he turned 23y today) when the compound interest bank has $500 greater than the simple interest bank?
: Remember years are rounded down
: Assume John is an alien
The answer is 196.
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1 solution
After t years, the amount in the simple interest account will be S = 2 0 + 0 . 6 t and the amount in the compound interest account will be C = 2 0 × 1 . 0 2 t .
We want to solve C − S = 5 0 0 . The only way to do this is numerically (though there are various options for exactly how); this yields 1 7 3 < t < 1 7 4 , so John will be 2 3 + 1 7 3 = 1 9 6 years old when this happens.