What is the formula to work out this kind of problem ????

Question

If a man invests X amount each year for Y years and get R%p.a. compound interest on the amount every year, then what is the maturity amount at the end of Y+1 years.
Please help !!

Answer 1

The formula is:

Future Value = X * [(1+R)^Y - 1]/R

The above is true if payments are made at the END of each year. However, if payments are made at the BEGINNING of each year, then the above formula becomes:

Future Value = X * ([(1+R)^Y - 1]/R)*(1+R)

So, depending on when payments are made, you need to use one of the above formula. Then you state that the value after Y+1 years if required, so multiply your Future Value by (1+R) again.

I am assuming that you are using an effective interest rate. In practice, rates are quoted as annual 'nominal' rates. However, for your example, I don't imagine you need to worry about nominal and effective rates since your compounding period is annual and your rate is essentially an effective rate.

Answer 2

THis you can work out with fairly simple maths.

At the end of year 1 his capital would be
X (1+r) where r is the rate of interest (eg if R=10% then r= 0.1)

At the end of year 2 his capital would be (again into (1+r)

X (1+r) (1+r) = X (1+r)^2


So at the end of Y+1 years his capital would be

X(1+r)^(y+1)

that is X times (1+r) to the power (y+1)

Answer 3

This sounds like a compound sum of an annuity problem. If you have Excel, then use the function FV.

FV(rate,nper,pmt,pv,type)

FV stands for future value. Maturity is a term associated with bonds. Please don't confuse the terminology.

Answer 4

end year 1 : X + R*X = X(1+R)

end year 2 : (X + previous Year )(1+R) = X(1+R) + X(1+R)(1+R)

etc etc

end year 3 : (X + previous Year )(1+R) = X(1+R) + X(1+R)(1+R) + X(1+R)(1+R)(1+R)

Sn = end of year n = Sum X(1+R)^ i ; i = 1 .... n

Answer 5

x times YR +x + 1R=

Answer 6

no free homework, thats cheating

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