In this section, we considered the case of regular deposits at the end of each m

Question

In this section, we considered the case of regular deposits at the end of each month. If deposits are made at the beginning of each month, then the formula is a bit different. The adjusted formula is Balance after t deposits

Here, r is the monthly interest rate (as a decimal), and t is the number of deposits. The extra factor of1 + r accounts for the interest earned on the deposit over the first month after it's made.

Suppose you deposit $200 at the beginning of each month for five years. Take the APR to be 7.2%. What is the future value? In other words, what will your account balance be at the end of the period?

(Fill in the blank below and round your answer to 2 decimal places.) Balance

Explanation / Answer

This is a form of annuity with deposits in the beginning of the month and maturity at the end of 5 years (60 months). Therefore, we deposit first amount at 0 month (i.e. beginning of the month) and continue to deposit it upto end of 59th month (i.e. beginning of 60th month)

Now, future value = Annuity Amount*[(1+Periodic Interest Rate)n-1]/[Periodic Interest Rate(1+Periodic Interest Raten)]

where n = no. of months i.e. 60 months

and Periodic Interest Rate = Monthly Interest Rate i.e. 7.2%/12 = 0.6%

Putting the values in above equation:

Future Value=200*[(1+0.6/100)60-1]/[0.6/100(1+.06/100)60] = 17072.80

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