Expert: Paul Klarreich - 10/4/2008

Question
Calculate the accumulated balance of the following:
a) £100 invested for 6 years at an effective rate of 5% per annum
b) £1200 invested for 8 years at an effective rate of interest of 3% per half year

c) £3500 invested for 12 years at an effective rate of interest of 2% per quarter year
d) £5000 invested for 15 years at an effective rate of interest 1.5% per month.

For part a) I think to get the answer you do 100 x (1.05)^6, and then for part b) 1200 x (1.03)^ 8 but then its per half year so I don't think its the same method. Thanks for your help.

Answer
Questioner:   Chandni
Category:  Advanced Math
Private:  No
 
Subject:  finance and investment maths
Question:  Calculate the accumulated balance of the following:
a) £100 invested for 6 years at an effective rate of 5% per annum
b) £1200 invested for 8 years at an effective rate of interest of 3% per half year

c) £3500 invested for 12 years at an effective rate of interest of 2% per quarter year
d) £5000 invested for 15 years at an effective rate of interest 1.5% per month.

For part a) I think to get the answer you do 100 x (1.05)^6, and then for part b) 1200 x (1.03)^ 8 but then its per half year so I don't think its the same method. Thanks for your help.
........................................................
Hi, Chandri,

This looks like an issue of Compound Interest, for which the rule is:

X = P(1 + r)^n, where:

P is the original amount invested.  
n is the number of compounding intervals, not always years.
r is the interest rate (as a decimal, like 0.05) for each of those intervals.

So, for part c, for example, you would do:

P = 3500 (don't get me started on those funny symbols.)
n = 48 quarters in 12 years.
r = 0.02, as you indicated, the interest rate per quarter.

X = 3500(1.02)^48

I think you can work out the others.