13 Sakira invested $£ 3550$ in a savings account for 3 years.
She was paid $2.6 \%$ per annum compound interest for each of the first 2 years. She was paid $R \%$ interest for the third year.
Sakira had $£ 3819.21$ in her savings account at the end of the 3 years.
Work out the value of $R$.
Give your answer correct to 1 decimal place.
Answer
\(\boxed{R = 2.2\%}\)
Step 1 ：Let's first calculate the amount in Sakira's account after the first 2 years with 2.6% compound interest: \(A = P(1 + r)^n\)
Step 2 ：\(A = 3550(1 + 0.026)^2\)
Step 3 ：\(A = 3736.9998\)
Step 4 ：Now, we need to find the interest rate for the third year by comparing the amount after the third year with the amount after the second year: \(3819.21 = 3736.9998(1 + R)\)
Step 5 ：\(R = \frac{3819.21}{3736.9998} - 1\)
Step 6 ：\(R = 0.02199898431891811\)
Step 7 ：Finally, we round the interest rate to 1 decimal place: \(R = 2.2\%\)
Step 8 ：\(\boxed{R = 2.2\%}\)
