Question

Suppose Evan deposited $10,000 into a savings account today. The account pays a nominal annual interest rate of 12%, but interest is compounded quarterly. Assuming that he makes no additional deposits into or withdrawals from the account, what will his ending balance be 10 years from today?

Answer 1

Compounding Technique

Interest is compounded when the amount earned on an initial deposit (initial principal) becomes part of the principal at the end of the first compounding period. The term principal refers to the amt. of money over which the interest is received. This compounding procedure may continue for an indefinite no. of years. The compounding of interest can be calculated by the following equation:-

  

Where,
A = amt. to be received at the end of the period
P = principal at the beginning of the period
i = rate of interest
n = no. of years

Now, in the financial institutions, very often the interest rates are compounded more than once in a year. savings institutions particularly compound interests semi-annually, quarterly or even monthly.

Quarterly Compounding means there are four compounding periods within the year. Instead of paying the interest once in a year, it is paid in 4 equal installments after every 3 months.

The effect of componding more than once in a year can also be expressed in the form of a formula. Specifically, the initial annual compounding formula is modified to the following formula :-

Here, m is the no. of times per year the compounding is made. For semi annual compounding m would be equal to 2 & for quarterly compounding m is equal to 4. In this case, we are simply required to divide the interest rate by the no. of times compounding occurs, that is & multiply the years by the no. of compounding periods per year, that is,  .

Now, in the above given problem, Evan deposited $10,000 in his savings account today & without any deposit or withdrawl he is supposed to get a lump sum amount at the end of the 10 years, with subject to an interest rate of 12%, compounded quarterly.

As we know, the formula :-

Here, P = $10,000,
i = 12% = 0.12,
m (the no. of compounding periods) = 4,
n = 10 years.

Therefore,
A = 10,000 {1+ (0.12/4)}4*10

A = 10,000 (1+ 0.03)40

A = 10,000 * (1.03)40 { The (1.03)40 can also be calculated using the POWER function of the MS - EXCEL}

A = 10,000 * 3.262038

A = 32620.38

Hence, Evan's ending balance in his savings account after 10 years from today will be $32620.38.