Correlation between rate of return from fixed deposit and its CAGR
Formula to calculate the compound interest from fixed deposit is:
Final value = Principal × [1+(r/n)]^(n×t)
Principal refers the invested amount.
‘n’ is compounding frequency, generally the value is 4 (quarterly for banks).
‘t’ is total period in years.
‘r’ is the annual interest rate.
Rate of return (in %) is calculated as:
[(Final value – Initial value) / Initial value] × 100
Compound Annual Growth Rate (CAGR)is used to measure the rate of return in a given period from an investment. It is a measure of the average yearly growth rate.
Formula to estimate CAGR is:
CAGR (%) = {[(Final value/Principal)^(1/t)] - 1} × 100
t = Number of years (Period).
Find the return and CAGR, if $100 is invested in fixed deposit at 7% interest rate for a period of 5 years.
n = 4((quarterly basis)
t = 5 years
r = 7/100 = 0.07
Principal = 100
Maturity (Final) value is calculated as:
= 100 × [1+(0.07/4)]^(4×5) = 141.47
So, the return after 5 years will be 41.47.
Tentative growth value of $100 in every year is given as:
Year Value
0 100.00
1 107.18
2 114.89
3 123.14
4 131.99
5 141.47
And the rate of return for 5 years is:
[(141.17 – 100) / 100] × 100 = 41.17 %.
And the rate of return for one year is:
41.17/5 = 8.234 %.
CAGR for the above return is estimated as:
CAGR (%) = {[(Final value/Principal)^(1/t)] - 1} × 100
Final value = 141.47
Principal = 100
t = 5 years
CAGR (%) = {[(141.47/100)^(1/5)] - 1 } × 100 = 7.18 %.
In the above fixed deposit calculation, at first year the growth of $100 is 107.18 or 7.18%.
To understand this, substitute t = 1 year in the compound interest formula then the final value is:
= 100 × [1+(0.07/4)]^(4×1) = 107.18.
In simple, every one year $100 gives 7.18 at an interest rate of 7%. This is taken account for CAGR calculation.
Hence, CAGR is the better parameter to estimate the real rate of return from an investment.