Question

Suppose you deposit $500 in an account at the end of this year, $400 at the end of next yer, and $300 at the end of the following year. The interest rate is 7.5%. How much will be in the account immediately after the third deposit is made? How much will be in the account at the end of three years if the deposits are made at the beginning of each year? Please show work and proper equation to use.

Answer 1

Solution :

Solution:

Situation: 1

Amount is deposited in an account at the end of the year and Simple Interest is earned:

Formula for calculation of interest = P*r

Where P= Prinicipal * rate of interest

Interest earned at the end of year 1 = 0

Interest earned at the end of year 2 = $ 500 * 7.5 % = $ 37.5

Interest earned at the end of year 3 = $ 400 * 7.5 % = $ 30

Total interest earned = $ 37.5 + $ 30 = $ 67.5 -------------   (A)

Amount in the account immediately after the third deposit = Principal + Interest earned

= $ 500 + $ 400 + $ 300 + $ 67.5 = $ 1267.5

Situation: 2

Amount is deposited in an account at the beginning of the year and Simple Interest is earned:

Formula for calculation of interest = P*r

Where P= Prinicipal * rate of interest

Interest earned at the end of year 1 = $ 500 * 7.5 % = $ 37.5

Interest earned at the end of year 2 = $ 400 * 7.5 % = $ 30

Interest earned at the end of year 3 = $ 300 * 7.5 % = $ 22.5

Total interest earned = $ 37.5 + $ 30 + $ 22.5 = $ 90 -------------   (B)

Amount in the account at the end of three years if the deposits are made at the beginning of each year = Principal + Interest earned

= $ 500 + $ 400 + $ 300 + $ 90 = $ 1290