Question

Suppose a deposit of $ 2 , 000 in a savings account that paid an annual interest rate r (compounded yearly) is worth $ 2 , 209 after 2 years. using the formula a = p ( 1 + r ) t , we have 2 , 209 = 2 , 000 ( 1 + r ) 2 solve for r to find the annual interest rate (to the nearest tenth).

Answer 1

5.1% (nearest tenth)

Explanation:

Annual Compound Interest Formula

`\large \text{$ \sf A=P\left(1+r\right)^(t) $}`

where:

• A = final amount
• P = principal amount
• r = interest rate (in decimal form)
• t = time (in years)

Given:

• A = $2,209
• P = $2,000
• t = 2 years

Substitute the given values into the formula and solve for r:

`\implies \sf 2209=2000\left(1+r\right)^(2)`

`\implies \sf (2209)/(2000)=(1+r)^2`

`\implies \sf 1.1045=(1+r)^2`

`\implies \sf √(1.1045)=1+r`

`\implies \sf r = √(1.1045)-1`

`\implies \sf r = 0.05095194942...`

`\implies \sf r = 5.095194942...\%`

Therefore, the annual interest rate is 5.1% (nearest tenth)