Question

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

Answer 1

Answer:

The rate of interest applied fro compound interest is 24.5 %  

The rate of interest applied simple interest is 37.5 %

Step-by-step 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 × $(1+\dfrac{\textrm rate}{100})^{\textrm Time}$

Or, $ 600 = $ 200 × $(1+\dfrac{\textrm R}{100})^{\textrm 2}$

Or, $\frac{600}{200}$ = $(1+\dfrac{\textrm R}{100})^{\textrm 2}$

Or, 3 = $(1+\dfrac{\textrm R}{100})^{\textrm 2}$

Or, $3^{\frac{1}{2}}$ = (1 +$\frac{R}{100}$)

Or, 1.245 = (1 +$\frac{R}{100}$)

or, 1.245 - 1 = $\dfrac{R}{100}$

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 = $\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}$

Or, $ 600 = $\dfrac{\textrm 800\times \textrm R\times \textrm 2}{100}$

Or,  $ 600 × 100 = $ 800 × R × 2

Or, R = $\frac{60000}{1600}$

∴ R = 37.5 %

So, The rate is 37.5 %

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