Question

Risa wanted to turn her 65,100 investment into 240,000 in 23 years. How much interest does she need to receive compounded semi-annually to reach her goal?



round your final answer to the nearest hundredth

Answer 1

Answer: 5.75%

Explanation:

Let the rate of interest be x

Since the amount is compounded semi-annually, the growth rate would be (1 + Rate/2) and the number of times compounded would be double the number of years. So

$A = P(1+\frac{x}{2})^{2t}$

$\Rightarrow 240000 = 65100(1+\frac{x}{2})^{2\times23}$

$\Rightarrow (1+\frac{x}{2})^{46}=\frac{240000}{65100} =\frac{800}{217}$

$\Rightarrow 1+\frac{x}{2} = \frac{\sqrt[46]{800}}{\sqrt[46]{217}}\approx1.028768$

$\Rightarrow\frac{x}{2} = 1.028768-1=0.028768$

$\Rightarrow x=0.028768\times2=0.057536$

Rate percentage = 0.057536 × 100% = 5.7536%

Rounding to nearest hundredth:

5.7536% → 5.75%

Hope my answer was of help