PLEASE HELP ME!!!!!!!!!!!!! How would you go about solving this?

Benjamin invests money in a bank account which gathers compound interest each year.
After 2 years there is $658.20 in the account. After 5 years there is $710.89 in the account.
Work out the annual interest rate of the bank account. Give your answer as a percentage to 1 d.p.
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Answer :

Answer:

2.6%

Step-by-step explanation:

Solution:

Let:

P = Principal (Amount invested initially)

R = Annual Interest Rate

T = Time (in years)

After 2 years, compounded amount is given by:

[tex]A_1 = P(1+R)^2\\\\\text{or, }658.2 = P(1+R)^2.........(1)[/tex]

After 5 years of investing in bank, compound amount is given by:

[tex]A_2=P(1+R)^5\\\\\text{or, }710.8=P(1+R)^5.........(2)[/tex]

Dividing equation(2) from equation(1),

[tex]\dfrac{A_2}{A_1}=\dfrac{P(1+R)^5}{P(1+R)^2}\\\\\\\text{or, }\dfrac{710.89}{658.2}=(1+R)^3\\\\\text{or, }1.08=(1+R)^3\\\\\text{or, }1+R=\sqrt[3]{1.08}=1.026\\\\\text{or, }R=0.026\\\\\text{or, }R=2.6\%[/tex]