(theory of mathematics interest)

Agus purchases a five year financial instrument having the following features :

(a) Agus receives payments of $1,000 at the end of each year for five years.

(b) These payments earn interest at an effective rate of 4% per annum. At the end of the year, this interest is REINVESTED at the effective rate of 5% per annum. Find the purchase price to Agus to produce a yield rate of 4% overall.

Hint : Draw the time line diagram for payment series and interest series to make it easy. Calculate the total accumulated value in five years (future value in year 5th). The purchase price is the present value of total accumulated value (FV in year 5th) that yields 4% over these five years.