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LUMPSUMS –INTEREST RATE AND PERIODS, AND NOMINAL AND EFFECTIVE INTEREST RATES
These calculations are quite challenging in an equation format but much easier with a financial calculator.
* see getting started
5.
Calculating the interest rate
An amount of R400,000 is invested in a savings
account that compounds interest monthly. After
one year the balance in the account is R464 301.81.
Calculate the nominal interest rate (i.e. the quoted
rate or APR).
The R400,000 is shown as a –ve as this is the cash
outflow required now.
6.
Calculating the periods
An amount of R100,000 was invested in an account
that accumulates interest at a rate of 14% per
annum, compounded quarterly. The balance in the
account, immediately after the latest quarter's
interest credit is R173,398.60. How long ago was
the amount invested?
Remember that because you have compounded
more than once a year (n x m in the formula) N is
not years but periods. So the answer is 16 ÷ 4 = 4
years.
7.
Calculating the effective rate
Calculate the effective rate of 13% per annum
compounded monthly.
This reflects the compounding periods per year (m in
the formula) and can be changed to any frequency.
8.
Calculating the nominal or annual percentage rate (APR)
Calculate the nominal rate (APR) of 14.9342% per
annum compounding monthly.
This reflects the compounding periods per year (m in
the formula) and can be changed to any frequency.
Colin C Smith 2010
HP10BII financial calculator
KEYS
C ALL
464,301.81 FV
400,000 +/‐ PV
1 x 12 N
I/YR
X 12
HP10BII financial calculator
KEYS
C ALL
173,398.60 FV
100,000 +/‐ PV
14 ÷ 4 I/YR
N
HP10BII financial calculator
KEYS
CLEAR ALL
13 NOM%
12 P/YR
EFF%
HP10BII financial calculator
KEYS
CLEAR ALL
14.9342 EFF%
12 P/YR
NOM%
DISPLAY
*Must not display BEGIN
0.00
464,301.81
‐400,000.00
12.00
1.25
15.00
DISPLAY
*Must not display BEGIN
0.00
173,398.60
‐100,000.00
3.50
16.00
DISPLAY
*Must not display BEGIN
0.00
13.00
12.00
13.80
DISPLAY
*Must not display BEGIN
0.00
14.93
12.00
14.00
4
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