Ryan was 8 when his parents invested $4000 in a certificate of deposit that pays 6%. If Ryan leaves the account alone until it reaches $10,000, how old will he be?

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Answer 1 · 2017-10-22T14:17:19

about $24$ $24$

Compund Interest Formula :

$Amount = Principle \cdot {(1 + Rate)}^{Time}$ $"Amount"="Principle"*(1+"Rate")^"Time"$

Here,

$$ 10000 = $ 4000 \cdot {(1 + 6 %)}^{t}$ $$10000=$4000 *(1+6%)^"t"$

$= \frac{$ 10000}{$ 4000} = \cdot {(1 + 0.6)}^{t}$ $=($10000)/($4000)= *(1+0.6)^"t"$

$= 2.5 = {1.06}^{t}$ $=2.5=1.06^t$

Take log of both sides:

$log ({1.06}^{x}) = log (2.5)$ $log(1.06^x)=log(2.5)$

$= x \cdot log (1.06) = log (2.5)$ $=x*log(1.06)=log(2.5)$

$= x = \frac{log (2.5)}{log (1.06)}$ $=x=log(2.5)/log(1.06)$

$= x \approx 15.73$ $=x~~15.73$

$therefore$ Ryan will be $8+15.73~~24$ years old then.