Angus has $3,000 he want to invest. What interest rate compounded continuously does an account need to offer so that Angus has $5,500 in 8 years?

The interest rate is 7.58%

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

A = P, where

∵ 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

→ Divide both sides by 3000

∴ =

→ Insert ㏑ in both sides

∵ ㏑( ) = ㏑()

→ Remember ㏑() = n

∴ ㏑( ) = 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%

250

step-by-step explanation:

1. d.90

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