Question

(6) Erik receives an eight-year annuity-immediate with monthly payments. The first payment is $300 and payments increase by $6 each month. The payments are deposited in an account earning interest at a nominal rate of 6% convertible monthly. What is the balance in the account at the end of the eight years

Answer 1

Answer:

• $70,264.03

Explanation:

You need to calculate the value of 8 × 12 = 96 different cash flows.

There is not a formula to calculate that, because the $6 dollar increase does not represent growing with a constant rate.

The monthly payments are:

Month            payment ($)

0 (today)             300

1                           306

2                          312

3                          318

n                          306 + 6 (n-1)

96 (last)               876

Then you must create a spreadsheet with these features:

• Five columns
• First column is the month, and starts with month 0 (today)
• Second column is the initial balance, the first balance is 0
• Third column is the interest: it is calculated as the monthly interest by the initial balance. The monthly interest is 6%/12 = 0.06/12 = 0.005
• Fourth column is the amount deposited: for month zero it is $300, and every month you add $6.
• Fith column is the final balance: it is the sum of the initial balance (second column) + interest (third column) + deposit (fourth colum)
• 96 rows: 8 years × 12months/year = 96 months.
• The initial balance of each row is equal to the final balance of the previous row.

Here a sample of the first three rows:

Month  Initial balance  Interest                    Deposit     Final balance

 0                  0                   0                          300          300

 1                 300             300×0.005 = 1.5    306          607.5

 2                607.5          607.5×0.005           312          922.54

When you do it up to the row 96, the final balance is the balance in the acccount at the end of the eight years.

The last row of your spreadsheet will show:

96           69,042.81      345.21                    876         70,264.03

Thus, the balance at the end of eight years will be $70,264.03