Question

Ted has always had difficulty saving money, so on June 1, Ted enrolls in a Christmas savings program at his local bank and deposits $750. That money is totally locked away until December 1 so that Ted can be certain that he will still have it once the holiday shopping season begins. Suppose that the annual rate of interest is 10 percent on ordinary savings accounts (that allow depositors to withdraw their money at any time). How much interest is Ted giving up by precommitting his money into the Christmas savings account for six months instead of depositing it into an ordinary savings account?
[Hint: If you invest X dollars at an annual interest rate of Y percent, you will receive interest equal to X × Y, where the interest rate Y is expressed as a decimal.]
$.___________.

Answer 1

Answer:

Ted is giving up an interest of 37.5 by pre-committing his money to a Christmas savings account

Explanation:

Step 1: Determine interest amount

The formula for calculating interest is as follows;

I=PRT

where;

I=interest

P=principal

R=annual interest rate

T=number of years

In our case;

P=750

R=10%=10/100=0.1

T=From June 1 to December 1=6 months=0.5 years

replacing;

I=(750×0.1×0.5)=$37.5

Step 2: Determine total amount Ted will have for the two scenarios

case 1

Christmas savings program=750

Ordinary savings account=(750+37.5)=787.5

Ted is giving up an interest of 37.5 by pre-committing his money to a Christmas savings account