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Fundamental Variables
The following four variables are fundamental to all compound
interest problems.
SINGLE-SUM PROBLEMS
Many business and investment decisions involve a single amount
of money that either exists now or will in the
future. Single-sum problems are generally classified into one of
the following two categories.
1. Computing the unknownfutur e value of a known single sum of
money that is invested now for a
certain number of periods at a certain interest rate.
2. Computing the unknown presentvalue of a known single sum of
money in the future that is discounted
for a certain number of periods at a certain interest rate.
When analyzing the information provided, determine first whether
the problem involves a future value or a present
value. Then apply the following general rules, depending on the
situation:
If solving for a future value, accumulate all cash flows to a
future point. In this instance, interest increases the
amounts or values over time so that the future value exceeds the
present value.
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If solving for a present value, discount all cash flows from the
future to the present. In this case, discounting
reduces the amounts or values, so that the present value is less
than the future amount.
Problem 1. B Co. wants to determine the future value of P50,000
invested for 5 years compounded annually at an
interest rate of 11%.
Answer: P84,253
Problem 2 C Company deposited P250 million in an account with
National Bank at the beginning of 2014 as a
commitment toward a power plant to be completed December 31,
2017. How much will the company have on
deposit at the end of 4 years if interest is 10%, compounded
semiannually?
Answer: P369,365,000
Problem 3. What is the present value of P84,253 to be received
or paid in 5 years discounted at 11% compounded
annually?
Answer: P50,000 (rounded by P.06)
Problem 4. Assume that your parents decides to give you P2,000
for a trip to Europe when you graduate from
college 3 years from now. They proposes to finance the trip by
investing a sum of money now at 8% compound
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interest that will provide you with P2,000 upon your graduation.
The only conditions are that you graduate and that
you tell him how much to invest now.
Answer: P1,587.66
Solving for Other Unknowns in Single-Sum Problems
Computation of the Number of Periods:
Problem 5. The Village wants to accumulate P70,000 for the
construction of a veterans monument in the town
square. At the beginning of the current year, the Village
deposited P47,811 in a memorial fund that earns 10%
interest compounded annually. How many years will it take to
accumulate P70,000 in the memorial fund?
Answer: 1Future Value Approach 1.46410
2. Present Value Approach .68301
Computation of the Interest Rate:Problem 6. Advanced Design,
Inc. needs P1,409,870 for basic research 5 years from now. The
company
currently has P800,000 to invest for that purpose. At what rate
of interest must it invest the P800,000 to fund basic
research projects of P1,409,870, 5 years from now?
Answer: 1Future Value Approach 1.76234
2. Present Value Approach .56743
