Answer:
Y = 479.17
Step-by-step explanation:
At the end of year 14, the balance from the deposits of X can be found using the annuity due formula:
A = P(1+r/n)((1 +r/n)^(nt) -1)/(r/n)
where P is the periodic payment, n is the number of payments and compoundings per year, t is the number of years, and r is the annual interest rate.
A = X(1.07)(1.07^14 -1)/0.07 ≈ 24.129022X
This accumulated amount continues to earn interest for the next 28 years, so will further be multiplied by 1.07^28. Then the final balance due to deposits of X will be ...
Ax = (24.129022X)(1.07^28) = 160.429967X
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The same annuity due formula can be used for the deposits of Y for the last 10 years of the interval:
Ay = Y(1.07)(1.07^10 -1)/.07 = 14.783599Y
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Now we can write the two equations in the two unknowns:
Ax +Ay = 100,000
X - Y = 100
From the latter, we have ...
X = Y +100
So the first equation becomes ...
160.429967(Y +100) +14.783599Y = 100000
175.213566Y +16,043.00 = 100,000
Y = (100,000 -16,043)/175.213566 ≈ 479.17
Y is 479.17
