Question

Daniel deposits a certain sum of money in a bank. If the simple interest rate of the bank decreases from 3.75% per annum to 3.5% per annum, Daniel's interest will increases by $50 in a year. Find the sum of money he deposits.

The answer is $20000 but I don't understand how. Please give a step-by-step explanation.

Answer 1

Answer: $20,000

Explanation:

Given

Interest decreases from 3.75% to 3.5% in a year

This change in the rate of interest brings a yield of 50$

Earlier interest was

`S.I_e=(P* 3.75* 1)/(100)`

Now, interest is

`S.I._n=(P* 3.5* 1)/(100)`

change gives 50$ i.e.

`\Rightarrow (P* 3.75* 1)/(100)-(P* 3.5* 1)/(100)=50\\\\\Rightarrow (P* (3.75-3.5)* 1)/(100)=50\\\\\Rightarrow P=(50* 100)/(0.25)=\$20,000`