Question

An investment of $2,000 is made and the interest rate is 1.5% per quarter. At the end of a year, determine the total amount available if:
(a) simple interest is used. (b) discrete compound interest is used. (c) continuous compound interest is used. (d) the nominal interest rate. (e) the effective discrete compound interest rate. (f) the effective continuous compound interest rate.

Answer 1

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a) Simple interest method:

First, converting R percent to r a decimal
r = R/100 = 1.5%/100 = 0.015 per quarter i. e 6% per year

Putting time into years for simplicity,
4 quarters/year = 1 years.

Solving our equation:
A = 2000(1 + (0.06× 1)) = 2120
A = $2,120.00
The total amount accrued, principal plus interest, from simple interest on a principal of $2,000.00 at a rate of 1.5% per quarter for 1 year (4 quarters) is $2,120.00.

b) Discrete compound interest

Total amount of value available at the end of year is = $2,000(1+1.5/4) power (4*1)

=$2,000 (3.574462)=$ 7,148

C) Continuous compound interest

Value at the end of year=$2,000 * (2.718) power 1.5

=$ 2000 * 4.4809= $8,961.98

D) Nominal interest rate

Formula: r= m [( 1+i) power 1/m] -1

r= 4 [(1+1.5) power 1/4]-1

= 1.4916%