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Practice Problems
Time Value of Money
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Problem 1 Your friend offers to sell his house to you for
P4.5 million. You make a down payment of
20% and agree to pay the balance throughequal monthly payments
over the next 30years at an annual interest of 7.5 %
compounded monthly. Your first payment ismade one month after
paying the downpayment. After several years, your friend asksyou to
pay off the remaining balance at theend of 8 years as he needs the
money tomigrate to the U.S. How much do you need topay at the end
of 8 years?
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Solution 1(b) Balance at the end of 8 years:
n = 8 yrs x 12 mos/yr = 96 mos
By Formula = PV (1 + i) - {pmt [(1+i) - 1]} / I
= 3.6M[1+(0.075/12)]- 25,171.72(1+0.075/12) /( 0.075/12 )
= 6,547,390.82 3,297,373. 47
= 3,250,017.34By Excel: FV(rate, nper, pmt, pv, type)
= FV( 0.075/12, 96, 0, -3600000,0)
- FV (0.075/12, 96, -25171.72, 0,0)
Or Excel :
= FV(0.075/12, 96, 25171.72, -3600000,0)
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Alternative solution for Balance Get the present value of
regular payments for
remaining 22 years:
By Formula: PV = {Pmt [1 (1 + i )]} / i= {25,171.72 [1 ( 1
+(0.075/12)}/(0.075/12)
= 3,250,017.04
By Excel: =PV(rate, nper, pmt, fv, type)
= PV (0.075/12, 22x12, -25171.72,0,0)
= 3,250,017.34
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Problem 1A
In order to pay your friend the total amount
by the eight year, you plan to borrow from a
local bank. You will borrow P3,250,000 at aninterest rate of
6.2% per annum compounded
quarterly, payable in 20 years.
So as not to upset your budget, you intend to
pay the bank semi-annually. How much will
your payment be each time?
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Solution to Problem 1A
Interest per quarter = 0.062/4 = 0.0155
Interest per 6 months:
= (1.0155) -1 = 0.03124
No. of periods = 20 yrs x 2 = 40
PV = 3,250,000
Pmt = pmt (rate, nper, pv, fv, type)
= pmt ( 0.03124, 40, -3250000, 0, 0)= 143,435.48
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Problem 2 Your existing credit card has an unpaid balance of
P60,000. The interest rate is 24 % per year,compounded monthly.
To reduce interestpayments you transfer the balance to a secondbank
which offers an introductory interest rate of2.4% per year
compounded monthly for the first
6 months, and increasing thereafter to 18% peryear compounded
monthly for the succeedingmonths. Assuming you make no
subsequent
payments, how much interest charges will yousave at the end of
one year by transferring thebalance to the second bank?
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