Question: User: Equation of Values
1. If money is worth 12% effective, what single payment at the end of 7 years would
replace the following debts:
a. P2,000 due in one year without interest;
B. P7,000 due in 8 years with accumulated interest from now at 12%
compounded semiannually.
2. A man borrows P20,000 today. He agrees to pay 5,000 in 2 years, P10,000 in 4 years
and the balance in 8 years. Find the final payment if interest is at 15% compounded
quarterly using the end of 4 years as focal date.
3. Daryl borrows P12, 000 on April 5, 2003. He pays P6, 000 on October 5, 2004. How
much will he have to pay to settle his debts on April 5, 2005 if he agreed to pay the interest
at 12% compounded semiannually?
4. A man owes P80, 000 due in 5 years with 8.5% interest compounded quarterly and
another sum due in 7 years at 9% compounded semiannually. He discharges the debts
in 6 years by a single payment of P300, 000. If money is worth 7% effective, find his other
debt.
5. Violy owes Angie the following debts:
a. P2,000 due in one year;
b. P3,500 due in 6 months with accumulated interest from today at 7.5%;
c. P3, 000 due in 18 months with accumulated interest from today at 10%
compounded semiannually.
Violy wishes to replace these debts with two equal payments at the end of 10 months and
three years, respectively. If money is worth 12% compounded monthly, how much is
each payment?
1. **Problem:** Find the single payment at the end of 7 years that replaces the debts:
a. P2,000 due in 1 year without interest.
b. P7,000 due in 8 years with 12% interest compounded semiannually.
2. **Formula and rules:**
- Future Value (FV) with compound interest: $$FV = PV \times \left(1 + \frac{i}{m}\right)^{mn}$$
- Present Value (PV) from future value: $$PV = \frac{FV}{\left(1 + \frac{i}{m}\right)^{mn}}$$
- Effective interest rate is given as 12% per year.
3. **Step a:** Calculate the value of P2,000 due in 1 year at the end of 7 years.
- Time from 1 year to 7 years is 6 years.
- Interest rate is 12% effective, so growth factor over 6 years is $$ (1 + 0.12)^6 $$
- Future value at 7 years: $$2000 \times (1.12)^6 = 2000 \times 1.9738 = 3947.6$$
4. **Step b:** Calculate the value of P7,000 due in 8 years at the end of 7 years.
- Since 8 years is 1 year after 7 years, we discount the P7,000 back 1 year at 12% compounded semiannually.
- Semiannual rate: $$\frac{0.12}{2} = 0.06$$
- Number of periods: $$2 \times 1 = 2$$
- Present value at 7 years: $$\frac{7000}{(1.06)^2} = \frac{7000}{1.1236} = 6227.4$$
5. **Step c:** Sum the two amounts at 7 years to find the single payment.
- Total payment: $$3947.6 + 6227.4 = 10175$$
**Final answer:** The single payment at the end of 7 years is approximately **P10,175**.