Mathematics of Deposit Rates?

K

kilyg2

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Could someone explain the following result from Bank of Scotland website Monthly Saver calculator. I put down an initial deposit of 20 euro's and then deposit 20 euro's per month at the EAR rate of 3.75% for 1 year. The Calculator then informs me I would earn interest of €5.62. How is this obtained? Would the calculation not be 260 * 0.0375= 9.75 - DIRT of 20% = €7.80. Could someone clear up this calculation?
 
You've done your calculations as though all the money you lodge will be in the account for a full year and will earn a year's interest, but this is not the case.

For simplicity, say you open an account on Jan 1st 2006.

By 31st Dec 2006, the initial €20 and the January payment of €20 (both lodged on 1st Jan) will have earned a full year's interest, but the €20 lodged on 1st July will only have earned interest for 6 months, and the €20 lodged on 1st Dec will only have earned interest for one month.
 
3.75% is the annual rate, but interest is calculated daily.
Only the initial EUR20 is there for the whole year, so only it gets the full 3.75%.
Successive installments get progressively less interest.
The last EUR20 earns practically no interest.
 
Thanks for that how then would the Compound Annual Rate work? Would a rate of 0.75% CAR for the same investment yield the following?

Month 1 Principal 100 Month 1 Interest 0.75
Month2 Principal 120.75 Month 2 Interest 0.906
Month 3 Principal 141.66 Month 3 Interest 1.0624
Etc

Is this correct or flawed?
 
Sorry I did that calculation based on saving €20 WEEKLY not monthly so would be €80 monthly
 
Sorry very muddled there for 0.75% CAR is the following correct?
Month 1 Principal 100 Month 1 Interest .75
Month 2 Principal 180.75 Month 2 Interest 1.355625
Month 3 Principal 262.11 Month 3 Interest 1.966
etc
 
The amount in your account after paying 20 a week for a year is:

P = 20 = amount paid per month
N = 12 = number of payments in the year
r = (1.0375)^(1/P) = monthly interest rate
^ = power function


P*r*(1 - r^(N))
--------------
1 - r

r works out at 1.0031 ( 0.3% interest per month )

This assumes payment of the EUR 20 at the start of each month.

Filling in gives:

20*(1.0031)*(1 - 1.0031^(12)) / ( -0.0031)

= EUR 244.8476

The EUR 20 initial payment has to be handled separately. This gives

20*(1.0375)

Adding that in gives:

265.5976

This gives interest of

EUR 5.60

The following are the amounts for each payment

20.7500 (*2 as there is EUR 40 at start of first month)
20.6864
20.6231
20.5599
20.4969
20.4341
20.3715
20.3091
20.2469
20.1849
20.1231
20.0615

The first payment gets the full 3.75% interest and the last payment gets almost no interest.

However, the bank of scotland calculator doesn't give interest on interest. This is in addition to messing up the monthly compound interest. This can be seen by checking the source code for their calculator.

Each month the interest is calculated by multiplying the amount in your account at the start of that month by (0.0375/12). This is then held in a separate interest total. The totals are then displayed on the web page after you press calculate. The total is just the sum of the deposited and the running interest total.
 
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