I have to replace shingles in 10 years on my house. Currently, they cost $145.00 per bundle of shingles. I will need at least 15 bundles. Based on assumption, of 1.5% interest that will be applied for 10 years. I wiould like to put a value amount of dollars into a sinking fund of 6% semiannually for 10 years to replace the shingles for my roof.

A) I would figure out that now, it would cost me $2,175.00 if I would buy them now.

B) How much would I have to pay in 10 years from now?

C) What is the difference between the two?

[QUOTE=chienrk;2009961]I have to replace shingles in 10 years on my house. Currently, they cost $145.00 per bundle of shingles. I will need at least 15 bundles. Based on assumption, of 1.5% interest that will be applied for 10 years. I wiould like to put a value amount of dollars into a sinking fund of 6% semiannually for 10 years to replace the shingles for my roof.

A) I would figure out that now, it would cost me $2,175.00 if I would buy them now.

B) How much would I have to pay in 10 years from now?

C) What is the difference between the two?

Future and Present Value of Money - Installment Loans - online financial calculator

Future Value Calculator

By now, you've no doubt obtained your answer via the online calculator suggested by Perito. But if this is a homework for some course, here goes:

A sinking fund payment is the payment amount that needs to be made in an ordinary annuity in order to achieve a certain amount in the future.

There are two types of annuities, an ordinary annuity and an annuity due. For an ordinary annuity, the payment is made at the end of the period. If it is made at the beginning of the period, then it is called an annuity due.

Back to your problem:

If you buy the shingles NOW, they will cost you $2175 if you buy 15 bundles. In ONE year, you will have to shell out MORE money for the shingles, namely 1.5% more which means your present value of the shingles times 101.5%

So in two years, your shingles will be costing you even more, namely $2175 x (1.015)^2
and in three years they will cost you even more money namely $2175 x (1.015)^3,
and in 10 years, you've guessed it...

Now to prepare for this, you want to put X in a sinking fund semiannually for 10 years to replace the shingles.

This means that for 10 years, you will regularly put X in that fund and wait for it to grow.

The first X that you put in your fund will have 19 periods to grow
The second X that you put will have only 19 periods to 'grow'
etc.

Therefore the final value of X will be X(1 + (1+i) + (1+i)^2 + (1+i)^3... (1+i)^19)

The terms within brackets are a geometric progression with first term 1, common ratio (1+1) and number of terms 20 and I is the interest per PERIOD.

Equate this with the amount you will have to shell out at the end of 10 years for your shingles and compute X.

If this is some finance course, you probably would prefer to forget the math and just focus on the formulae:

Then, for the sinking fund:

FV = PM((1+r)^N - 1) / r

where PM = payment amount
r = period interest rate, here 6% / 2
N = number of years times the number of payments made per year

This will have to be equated with another formula for the FV of the shingles:

FV which is FV = PV (1+r)^N where this time, PV is present value of the shingles, N is 10 years and r is your 'inflation rate'.