Predicting Change

Question

Suppose $6,300 is invested in an annually compounded account at 4%. Approximately how long will it take for the balance to reach $15,750? (Round the answer to the nearest tenth of a year.)

Answer 1

P(t) = P₀(1 + rate)^t

• P(t) = priniciple in t years = $15750
• P0 = starting principle = $6300
• rate = 4% = 0.04
• t = years

 

P(t) = P₀(1 + rate)^t

$15,750 = $6300(1 + 0.04)^t

$15750/$6300 = (1.04)^t

log(15750/6300) = log(1.04^t)

log(15750/6300) = t·log(1.04)    [Log property: log(a^b) = b·log(a)]

log(15750/6300)/log(1.04) = t

 

Use your calculator to compute the answer.  You can use any base log.  Round to teh nearest tenth.