Question

4. Two savings accounts each start with a $200 principal and have an interest rate of 5%. One account earns simple interest and the other is compounded annually. Which account will earn more interest over 10 years? How much more?​

Answer 1

The compounded annually account will earn more interest over 10 years

Explanation:

The rule of the simple interest is I = Prt, where

• P is the original value

• r is the rate in decimal

• t is the time

The rule of the compounded interest is A = P
`(1+(r)/(n))^(nt)`, where

• A is the new value

• P is the original value

• r is the rate in decimal

• n is the number of periods

• t is the time

The interest I = A - P

∵ Each account start with $200

∴ P = 200

∵ They have an interest rate of 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∵ One account earns simple interest and the other is compounded

annually

∴ n = 1 ⇒ compounded annually

∵ The time is 10 years

∴ t = 10

→ Substitute these values in the two rules above

∵ I = 200(0.05)(10)

∴ I = 100

∴ The simple interest = $100

∵ I = A - P

∵ A = 200
`(1+(0.05)/(1))^(1(10))`

∴ A = 325.7789254

∵ I = 325.7789254 - 200

∴ I = 125.7789254

∴ The compounded interest = $125.7789254

∵ The simple interest is $100

∵ The compounded interest is $125.7789254

∵ $125.7789254 > $100

∴ The compounded annually account will earn more interest

over 10 years