Question

consider a $1000 deposit earning 6.0% interest per year for five years. interest earned on the original deposit excluding interest earned on interest is $300.00 and total interest earned is more than $335 if interest is compounded annually

true or false?

Answer 1

Solution:

Calculation of Simple Interest:

The simple interest is calculated using the following formula

I = P * R *T

Where I = Interest ; P = Amount of deposit

R = Rate of interest ; T = time period in years

As per the information given in the Question we have

P = $ 1,000 ; R = 6 % per year ; T = 5 years

Therefore, the Interest earned during the period of five years = $ 1,000 * 6 % * 5

= $ 300

Thus the simple interest earned on a deposit of $ 1,000 for a period of 5 years = $ 300

Calculation of Compound Interest:

The simple interest is calculated using the following formula

I = [ P * ( 1 + r ) ^t ] - P

Where I = Interest ; P = Amount of deposit

r = Rate of interest ; t = time period in years

As per the information given in the Question we have

P = $ 1,000 ; r = 6 % = 0.06    ; T = 5 years

Therefore, the Compound Interest earned during the period of five years is

= [ $ 1,000 * ( 1 + 0.06 ) ⁵ ] - $ 1,000

= [ $ 1,000 * ( 1.06 ) ⁵ ] - $ 1,000

= [ $ 1,000 * 1.3382 ] - $ 1,000

= $ 1,338.2 - $ 1,000

= $ 338.2

The compound Interest earned on a deposit of $ 1,000 for a period of 5 years = $ 338.2

Thus the statement in the question is TRUE.

Therefore interest earned on the original deposit excluding interest earned on interest ( i.e., Simple Interest ) is $300.00 and total interest earned is more than $335 = $ 338.20 if interest is compounded annually

Note : ( 1.06 ) ⁵ is calculated using the excel formula =POWER(Number,Power) = POWER(1.06,5) = 1.3382