Question 1173376: A person wants to deposit $10,000 per year for 6 years. If interest is earned at the rate of 10 percent per year, compute the amount to which the deposits will grow by the end of the 6 years if:
(a) Deposits of $10,000 are made at the end of each year with interest compounded annually.
(b) Deposits of $5,000 are made at the end of each 6-month period with interest com¬pounded semiannually.
(c) Deposits of $2,500 are made at the end of every quarter with interest compounded
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down each scenario to calculate the future value of the deposits.
a) Annual Deposits of $10,000, 10% Annual Interest
Payment (PMT): $10,000
Interest Rate (r): 10% or 0.10
Number of Years (n): 6
We'll use the future value of an ordinary annuity formula:
FV = PMT * [((1 + r)^n - 1) / r]
FV = $10,000 * [((1 + 0.10)^6 - 1) / 0.10]
FV = $10,000 * [(1.10^6 - 1) / 0.10]
FV = $10,000 * [(1.771561 - 1) / 0.10]
FV = $10,000 * [0.771561 / 0.10]
FV = $10,000 * 7.71561
FV = $77,156.10
b) Semiannual Deposits of $5,000, 10% Annual Interest (5% per Period)
Payment (PMT): $5,000
Interest Rate per Period (r): 10% / 2 = 5% or 0.05
Number of Periods (n): 6 years * 2 periods/year = 12 periods
FV = PMT * [((1 + r)^n - 1) / r]
FV = $5,000 * [((1 + 0.05)^12 - 1) / 0.05]
FV = $5,000 * [(1.05^12 - 1) / 0.05]
FV = $5,000 * [(1.795856 - 1) / 0.05]
FV = $5,000 * [0.795856 / 0.05]
FV = $5,000 * 15.917127
FV = $79,585.64
c) Quarterly Deposits of $2,500, 10% Annual Interest (2.5% per Period)
Payment (PMT): $2,500
Interest Rate per Period (r): 10% / 4 = 2.5% or 0.025
Number of Periods (n): 6 years * 4 periods/year = 24 periods
FV = PMT * [((1 + r)^n - 1) / r]
FV = $2,500 * [((1 + 0.025)^24 - 1) / 0.025]
FV = $2,500 * [(1.025^24 - 1) / 0.025]
FV = $2,500 * [(1.808734 - 1) / 0.025]
FV = $2,500 * [0.808734 / 0.025]
FV = $2,500 * 32.349377
FV = $80,873.44
Results:
(a) Annual Deposits: $77,156.10
(b) Semiannual Deposits: $79,585.64
(c) Quarterly Deposits: $80,873.44
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