Solutions to TVM Practice Set II
1.
In this problem you are solving for the monthly rate of return and then the yearly rate
of return.
There are 228 months in 19 years (19 * 12 = 228).
a)
To determine the monthly rate of return:
1
)
100
,
1
$
438
,
13
$
(
228
1

=
1.104%
N = 228, PV = $1,100, FV = $13,438; compute I
b)
To determine the yearly rate of return :
1
)
100
,
1
$
438
,
13
$
(
19
1

=
14.079%
N = 19, PV = $1,100, FV = $13,438; compute I
2.
You should disagree with Jim.
You do not owe $1,900 for the entire year since you
are making monthly payments that would reduce the outstanding loan balance.
If
your total interest payments are $380, the true rate of interest is much higher than
20%.
You would need to set up the problem and solve for r (a monthly rate) in the
PVIFA equation.
You could convert the monthly rate to an A.P.R. by multiplying it
by 12.
The true A.P.R. is 35.07%, not 20% as Jim is suggesting.
=> $1,900 = $190 *
[
(
)
]
1
1
1
12

+
r
r
Now, use a financial calculator to solve for the monthly rate of interest (r).
On a financial calculator:
N = 12, PV = 1,900, PMT = 190; compute I
=> r = 2.923% per month
=>
2.923% * 12 = 35.07% APR
=> The E.A.R on the loan would be found as follows:
(1.02923)
12
–1 =
41.30%
3.
Here you must solve for the E.A.R of an
annuity due
.
The easiest way to solve this
problem is to set your calculator to BEGIN mode, directly solve for the monthly rate,
and then convert the monthly rate to an effective rate.
ON BEGIN MODE:
N = 24, PV = $1150, PMT = $60; compute I
I = 2.0632% per month
Convert to an E.A.R.:
(1.020632)
12
–1 =
27.77%
F301 TVM practice set II solutions
1