(6) Erik receives an eight-year annuity-immediate with monthly payments. The first payment is $300 and payments increase by $6 e

Question

14 days ago

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(6) Erik receives an eight-year annuity-immediate with monthly payments. The first payment is $300 and payments increase by $6 e

ach 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

Business

1 answer:

Mariulka [3.1K] · Answer 1 · 2026-03-22T14:24:47+03:00

Answer:

$70,264.03

Explanation:

To compute the value, 8 × 12 = 96 distinct cash flows need to be evaluated.

There's no single formula for this case, as the $6 increase does not follow a constant growth rate.

The monthly payment schedule is:

Month payment ($)

0 (today) 300

1 306

2 312

3 318

n 306 + 6 (n-1)

96 (last) 876

Then create a spreadsheet reflecting these details:

Five columns
The first column indicates the month starting at month 0 (today)
The second column represents the initial balance, starting with 0
The third column calculates interest based on the monthly interest of 6% convertible monthly: 0.06/12 = 0.005.
The fourth column reflects the deposit amount; $300 in month zero, increasing by $6 each following month.
The final balance in column five constitutes the initial balance (column two) + interest (column three) + deposit (column four).
Total rows needed: 96, for 8 years × 12 months/year = 96 months.
Each row's initial balance equals the previous row's final balance.

Here is a sample for 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

Continue this process until you complete the 96 rows to arrive at the account balance after eight years, which is reflected as the final row shows

96 69,042.81 345.21 876 70,264.03

Thus, the balance in the account at the end of eight years totals to $70,264.03