Question

MC algo 4-3 Simple Vs. Compound Interest You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to invest $2,900 today and both accounts have an annual interest rate of 8 percent. How much more interest will you receive in the 11th year in the account that pays compound interest? Multiple Choice $268.87 $286,03 $281.72 $232.00 O$28254

Answer 1

Simple interest

= Principal x Rate x Time / 12

In Simple interest, interest is always calculated on the principal amount and interest on interest is not charged

So, Simple interest in 11^th Year

= $2,900 x 8% x 1 / 12 ( Since interest is calculated for one year only, year is taken as 1)

= $232

Compound interest for a year

= Principal x ( 1 + Rate of interest) ^ Number of years - Principal x ( 1 + Rate of interest) ^ (Number of years -   1)

In the case of compound interest, interest on interest is alos calculated which results in multiple times charging of interest

The above equation [Principal x ( 1 + Rate of interest) ^ Number of years] gives future value of the Principal if it is invested for a specified period. So, to calculate the interest for 11^th year, we need to calculate the future value at the end of 11^th year and deduct future value at the end of 10^th year so that interest for the year is calculated

= $2,900 x ( 1.08 ^ 11) - $2,900 x ( 1.08 ^ 10 )

= $ 6,761.75 - $ 6,260.88

= $500.87

So, Excess interest received over simple interest

= Compound interest – Simple interest

= $ 500.87 - $232.00

= $268.87

So, as per above calculations, option A is the correct option