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.