Vic French mad deposits of 5000 at the end of each quarter to book bank, which pays 8% intrest compounded quarterly. After 3 years, Victor made no more deposits. What will be the balance in the account 2 years after the last deposit? I do not understand how to figure out this problem whats so ever. I have been trying to figure out this out via texas instrument calculator using the N,I/Y,PV,PMT.FV Help
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To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value or balance in the account
P = the principal or starting amount
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal (P) is $5,000 (the amount of each deposit), the annual interest rate (r) is 8% (or 0.08), and the interest is compounded quarterly, meaning n = 4 (four quarters in a year).
Let's break down the problem step by step:
Step 1: Calculate the number of quarters for the full period of 3 years (12 quarters in a year) and the number of quarters after the last deposit.
3 years = 3 x 12 = 36 quarters
2 years after the last deposit = 2 x 4 = 8 quarters
Step 2: Calculate the total balance after the last deposit.
Using the formula, we need to find A after the 36 quarters of deposits:
A = 5000(1 + 0.08/4)^(4 x 36)
A = 5000(1.02)^144
Using a calculator to evaluate (1.02)^144, we find it to be approximately 2.208040283.
A = 5000(2.208040283)
A ≈ $11,040.20
Step 3: Calculate the balance after the additional 8 quarters (2 years) without any deposits.
Using the formula again, now we have P = $11,040.20, n = 4 (quarterly compounding), r = 0.08, and t = 8:
A = 11040.20(1 + 0.08/4)^(4 x 8)
A = 11040.20(1.02)^32
Using a calculator to evaluate (1.02)^32, we find it to be approximately 1.856161008.
A = 11040.20(1.856161008)
A ≈ $20,466.13
Therefore, the balance in the account 2 years after the last deposit will be approximately $20,466.13.
I hope this explanation helps you understand how to solve compound interest problems. Let me know if you need any further assistance!