Question

PLEASE HELP ASAP!!

A savings account starts with $420. After 6 years of continuously compounding at an interest rate, r, the account has a balance of $1,300. What is the interest rate percentage (do not type % it is already there)? Round answer to the nearest hundredth.

Answer 1

18.83% (nearest hundredth)

Explanation:

Continuous Compounding Formula

`\sf A=P(e)^(rt)`

where:

• A = amount
• P = principal (initial amount)
• e = mathematical constant ≈ 2.7183
• r = interest rate (in decimal form)
• t = time in years

Given:

• A = $1,300
• P = $420
• t = 6 years

Substituting given values into the formula:

`\sf \implies 1300=420(e)^(6r)`

`\sf \implies (1300)/(420)=e^(6r)`

`\sf \implies e^(6r)=(65)/(21)`

Taking natural logs of both sides:

`\sf \implies \ln e^(6r)=\ln (65)/(21)`

`\sf \implies 6r\ln e=\ln (65)/(21)`

`\sf \implies 6r(1)=\ln (65)/(21)`

`\sf \implies 6r=\ln (65)/(21)`

`\sf \implies r=\frac16 \ln (65)/(21)`

`\sf \implies r=0.1883108054...`

Therefore, the interest rate is 18.83% (nearest hundredth)