Question

How long will it take your money to double if you put $500 into an account compounded quarterly at 2.9%?

Answer 1

Answer: About 24 years

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Work Shown:

A = P*(1+r/n)^(n*t)

1000 = 500*(1+0.029/4)^(4*t)

1000 = 500*(1.00725)^(4*t)

1000/500 = (1.00725)^(4*t)

2 = (1.00725)^(4*t)

log(2) = log( 1.00725^(4*t) )

log(2) = 4*t*log( 1.00725 )

4*t*log( 1.00725 ) = log(2)

t = log(2)/( 4*log( 1.00725 ) )

t = 23.9881659971072 The value is approximate

t = 24 when rounding to the nearest full year

It takes approximately 24 years to double your money.