Question

Suppose $1,000 was deposited into an account compounded quarterly that grew to $1,490 at rate of 6%. How long did it take for this to occur?

Answer 1

`t = ln(A/P) / n[ln(1 + r/n)]\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.06/4)] )\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.015)] )\\t = 6.7 years`

It would take around 6 years 8 months to get $1,490 from $1,000 at 6%.

I hope I've helped! :)

Answer 2

A (1 + i)^n = 1490 time for amount to reach 1490

(1 + i)^n = 1.49 since A = $1000

n log (1 + .06/4) = log 1.49 take log of both sides at 1.5% per quarter

n = log (1.49) / log 1.015 = 26.78 periods or 6.695 years

(compare to 6.843 years compounded annually)