A deposit in a bank yields a simple yearly interest rate of r. This means that,

Question

A deposit in a bank yields a simple yearly interest rate ofr. This means that, if you deposit xdollars in it, after t years (t can take anypositive real value, of course: for instance, t = .25means 3 months), your capital has become y = x ( 1 +rt) Suppose r - 0.05 (that's a 5% interest rate). Howmuch time do you need to double your initial investmentx? A deposit in a bank yields a simple yearly interest rate ofr. This means that, if you deposit xdollars in it, after t years (t can take anypositive real value, of course: for instance, t = .25means 3 months), your capital has become y = x ( 1 +rt) Suppose r - 0.05 (that's a 5% interest rate). Howmuch time do you need to double your initial investmentx?

Explanation / Answer

The equation isn't quite right. It should read Y = X(1+r)t Assume the following: r = 0.05 (i.e. 5%) X = 1 Y = 2 (i.e. the investment has doubled) You can now solve for t. 2 = 1(1+0.05)t 2 = 1.05t t = 14.21 years (There's also a general rule of thumb where you divide 72 by theinterest rate (in percentage) (i.e. 72/5)).

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