Compound Interest Calculation

m00c0w04

I was wondering if someone could show me how to calculate compound interest in this scenario. This is a hypothetical calculation and simply a curiosity of mine. Say you had an initial sum of £1000 in a bank and you added £1 a day for a year with an interest rate of 4% p.a. How would you calculate the overall amount after a year?

Many thanks.

grumbler

For exact formula look here: 'compound interest-how do I work it out?'

For your example:
q=1.04^(1/365)=1.000107
£1*(q+q^2+q^3+…+q^365)=£1*q*(q^365-1)/(q-1)=£372.27
Total amount after a year is £1000*1.04+£372.27=£1412.27
Total interest is £40+(£372.27-£365)=£47.27
For low interest rates (below 10% AER) albertross' method works fine. For higher rates discrepancy will rise.

See also Regular Savings Accounts discussion

exil

Basically, take the interest rate per period in the form 1.01 (1%), 1.02 (2%) etc

Then raise that to the power of the number of periods in the loan/investment

2.00 would be 100% interest. 2.00^1 = 2.00, 2.00^2 = 4.00, and so on. So at 100%,
£100 becomes £200 after 1 year, £400 after 2....

Excel can do this calculations easily

In cell A1 put the interest rate in %
In cell A2 put the number of periods
In cell A3 put the original amount
In cell A4 put =A3*((1+A1)^A2)

grumbler

exil wrote:

Basically, take the interest rate per period in the form 1.01 (1%), 1.02 (2%) etc

Then raise that to the power of the number of periods in the loan/investment

2.00 would be 100% interest. 2.00^1 = 2.00, 2.00^2 = 4.00, and so on. So at 100%,
£100 becomes £200 after 1 year, £400 after 2....

Excel can do this calculations easily

In cell A1 put the interest rate in %
In cell A2 put the number of periods
In cell A3 put the original amount
In cell A4 put =A3*((1+A1)^A2)

Have not you missed the essential point (your post dosn't give an answer to this)?

m00c0w04 wrote:

...and you added £1 a day for a year ...

P.S. There is special Excel function for regular savings - FV. It 'returns the future value of an investment based on periodic, constant payments and a constant interest rate.'