Calculate Maturity Value for a Simple Interest Account
by Hanis
(Malaysia)
Question
Razifah deposited $2000 in an account at rate of 3.75% simple interest. 8 months later, she deposited another $3000 into account. Find the total amount in the account three years after the first deposit.
Answer
After understanding the question, it is better to split the solution into two parts before we can get the answer. These parts are:
1) Find the total amount after 8 months
2) Find the total amount for the rest of the period
Since we are finding the total amount, we can use the maturity value formula shown below:
You can see the
lesson on simple interest to learn more about this formula.
1) Find the total amount after 8 months.It is important to know that the interest 3.75% is on per year basis (or per annum) unless stated otherwise. Therefore, it is important to convert 8 months to years. Since 1 year consists of 12 months, we divide 8 months with
12. Here's how:
Next, we need to convert 3.75% to a decimal by dividing it with
100. Here's how:
Alright, we are all set to calculate the total amount in the account after
^{8}/
_{12} year. These are the information that we have:
- Principal, P = $2000
- Interest rate, r = 0.0375
- Duration/Period, t = ^{8}/_{12}
Substituting these values into the maturity value formula:
Hence, after 8 months, the total amount in the account is $2050. Let's go to the second part:
2) Find the total amount for the remaining periodNow, after covering the first 8 months. Let's find the maturity value for the rest of the remaining period. Since, 3 years has 36 months (3 x 12), the:
Next, we have to convert 28 months to year by dividing it with
12:
Razifah deposit another $3000 into her account. Therefore, the amount of money in her account after 8 months will be:
Hence, we have the following information:
- Principal, P = $5050
- Interest rate, r = 0.0375
- Duration/Period, t = ^{28}/_{12}
We can calculate for the maturity value after 3 years using the above information. This is shown below:
Therefore, the total amount in the account three years after the first deposit is
$5491.88.