Question

Find the period.Principal = 9300 rupeesAnnual rate of interest = 13%Total amount = 17,763 rupeesPeriod =yearsStuck? Review related articles/videos or use a hint.

Answer 1

The formula for compound interest is:

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

Where A is the current amount, P is the initial amount, r is the interest rate, n is the number of times the interest is applied in a period, and t is the period. Then, in our problem,

`A=17763,P=9300,n=1,r=0.13`

We need to solve for t, as follows:

`\begin{gathered} A=P(1+r)^t,n=1 \\ \Rightarrow(1+r)^t=(A)/(P) \\ \Rightarrow\ln ((1+r)^t)=\ln ((A)/(P)) \\ \Rightarrow t\ln (1+r)=\ln ((A)/(P)) \\ \Rightarrow t=(\ln((A)/(P)))/(\ln(1+r)) \end{gathered}`

Therefore (using numeric values),

`t=(\ln ((17763)/(9300)))/(\ln (1.13))\approx5.3`

Therefore, we will reach that total amount after 5.3 years of compound interest.