TVM Sample Problems
2
3.
How many years will it take for your savings account to accumulate $1m if it
pays 4% interest p.a. compounded semiannually and you deposit $10k every 6-
months at the end of the 6-month period?
0
PMT = (-)10,000
r = 4%
FV = $1m
n = ?
1
2
3
4
5
n - 1
n - 2
4.
Today you deposited $1,300 in a bank that pays 5% p.a., compounded
quarterly. How much money would you have in this account 20 months from
now?
0
1
2
5
6
7
r
nominal
= 5%
PV = $1,300
m = 4, T = 20/12 = 1.666667
n = m x T = 6.666667
FV = ?
n = 6.666667
r
periodic
= r
nominal
/m = 5%/4 = 1.25%
P/Y=1, N=6.666667, I/Y=1.25, PV=1300; CPT,FV: FV =
$1,412.25
OR
P/Y=4, N=6.666667, I/Y=5, PV=1300; CPT,FV: FV =
$1,412.25
a) Find number of periods
r
periodic
= r
nominal
/ m = 4%/2 = 2%
P/Y=1, I/Y= 2,
PMT=-10000, FV=1000000; CPT,N: N = 55.48 periods
OR
P/Y=2, I/Y= 4,
PMT=-10000, FV=1000000; CPT,N: N = 55.48 periods
b) Find number of years
Years = N/m = 55.48/2 =
27.74 years