Question

How long would it take $3,100 to grow to $8,200 if the annual rate is 3.6% and interest in compounded monthly

Answer 1

Principal amount (P) = $3100
Final amount (A) = $8200
Interest rate (r) = 3.6% = 0.036
Interest is compounded monthly. So n = 12

Now we can apply compound interest formula as

`A = P(1+ (r)/(n))^(nt)`
Where t is time
Now we can place the value of A , P , r and n

`8200 = 3100(1+ (0.036)/(12))^(12*t)`
Now we can simplify it as

`(8200)/(3100) = (1+0.003)^(12t)`

`2.6452 = (1.003)^(12t)`

On taking logarithmic function(ln) on both sides

`ln(2.6452) = ln(1.003)^(12t)`
Now we can use basic property of ln function as
`ln(x^a) = aln(x)`
So we can above expression as

`ln(2.6452) = 12t * ln(1.003)`

`(ln(2.6452))/(ln(1.003)) = 12t`

`324.735 = 12t`
So
`t = (324.75)/(12) = 27.06`