Question

5. An $800 deposit for 24
months earned $200 in
interest

Answer 1

The rate of interest applied fro compound interest is 24.5 %

The rate of interest applied simple interest is 37.5 %

Explanation:

Given as :

The Principal amount that is deposited = $ 800

The Time period = 24 months = 2 years

The Interest earn = $ 200

Let the rate of interest = R %

So, The Amount = Principal deposited - interest earn

Or, A = $ 800 - $ 200

∴ Amount = $ 600

From compounded method

Amount = Principal ×
`(1+(\textrm rate)/(100))^(\textrm Time)`

Or, $ 600 = $ 200 ×
`(1+(\textrm R)/(100))^(\textrm 2)`

Or,
`(600)/(200)` =
`(1+(\textrm R)/(100))^(\textrm 2)`

Or, 3 =
`(1+(\textrm R)/(100))^(\textrm 2)`

Or,
`3^{(1)/(2)}` = (1 +
`(R)/(100)`)

Or, 1.245 = (1 +
`(R)/(100)`)

or, 1.245 - 1 =
`(R)/(100)`

or, 0.245 × 100 = R

So, the rate is = 24.5 %

Hence The rate of interest applied fro compound interest is 24.5 % Answer

From Simple Interest method

Simple Interest =
`(\textrm Principal* \textrm Rate* \textrm Time)/(100)`

Or, $ 600 =
`(\textrm 800* \textrm R* \textrm 2)/(100)`

Or, $ 600 × 100 = $ 800 × R × 2

Or, R =
`(60000)/(1600)`

∴ R = 37.5 %

So, The rate is 37.5 %

Hence The rate of interest applied simple interest is 37.5 %Answer