Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P[tex]e^{rt}[/tex], where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ Angus has $3,000 he want to invest
∴ P = 3000
∵ The interest rate is compounded continuously
∵ Angus has $5,500 in 8 years
∴ A = 5500
∴ t = 8
→ Substitute them in the rule above to find r
∵ 5500 = 3000[tex]e^{8r}[/tex]
→ Divide both sides by 3000
∴ [tex]\frac{11}{6}[/tex] = [tex]e^{8r}[/tex]
→ Insert ㏑ in both sides
∵ ㏑( [tex]\frac{11}{6}[/tex] ) = ㏑([tex]e^{8r}[/tex])
→ Remember ㏑([tex]e^{n}[/tex]) = n
∴ ㏑( [tex]\frac{11}{6}[/tex] ) = 8r
→ Divide both sides by 8
∴ 0.07576697545 = r
→ Multiply it by 100% to change it to a percentage
∴ r = 0.07576697545 × 100%
∴ r = 7.576697545 %
→ Round it to the nearest hundredth
∴ r ≅ 7.58
∴ The interest rate is 7.58%
