Find how many years it will take 15500 to increase to 30000

Find how many years it will take $15,500 to increase to $30,000 in a savings account with a 6.75 % interest rate with 4 compounding yearly. A = P (1 + r/n)^nt

Solution

Given that A = P [ 1 + (r/n)]^nt

Given that A = 30000

               P = 15500

                r = 6.75 % = 0.0675

               n = 4

Then,

A = P [ 1 + (r/n)]^nt

Take logarithm on both sides,

log A = log P + log [ 1 + (r/n)]^nt

log A = log P + nt log [1+(r/n)]

nt log [1+(r/n)] = log A - log P

t = [log A - log P] / {n. log [1+(r/n)] }

Substitute all the given values,

Then,

t = [log 30000 - log 15500] / {4. log [1+(0.0675/4)] }

= 9.86 yrs

t = 9.86 yrs

Therefore,

required time = 9.86 yrs