Question

A series of 25 end-of-year deposits beginning with $1976 at the end of year 1 and increasing by $290 per year with a 11% interest rate. What Uniform Series of deposits would result in the same cumulative balance? $

Answer 1

ANSWER:

IN ORDER TO FIND OUT THE UNIFORM SERIES OF DEPOSITS AT 11% INTEREST RATE , WE WILL HAVE TO EQUATE THE PRESENT WORTH OF BOTH THE DEPOSITS EQUAL.

PW OF DEPOSIT 1 = INITIAL AMOUNT(P/A,I,N) + GRADIENT AMOUNT(A/G,I,N)

INITIAL AMOUNT = 1976 , I = 11% , N = 25

GRADIENT AMOUNT = 290

PW OF DEPOSIT 1 = 1976(P/A,11%,25) + 290(P/G,11%,25) = 1976 * 8.422 + 290 * 59.832 = 16,641.872 + 17,351.28 = $33,993.152

NOW IN ORDER TO FIND THE UNIFORM SERIES OF DEPOSITS , THERE PRESENT VALUE WILL BE EQUAL TO $33,993.152

33,993.152 = AMOUNT(P/A,11%,25)

33,993.152 = AMOUNT * 8.422

AMOUNT = 33,933.152 / 8.422 = $4029.108

THEREFORE THE UNIFORM AMOUNT TO BE DEPOSITED IS $4029.108