Question

Eloise plans to accumulate 100,000 at the end of 42 years. She makes the following deposits: X at the beginning of years 1-14; No deposits at the beginning of years 15-32; and Y at the beginning of years 33-42. The annual effective interest rate is 7%. X – Y = 100. Calculate Y.

Answer 1

Answer:

Y=$325.17

Explanation:

Both X and Y are annuity due payments.

For X, n=14,r=7%,compounded time =28yrs

Therefore

$FVx=X[\frac{(1+r)^{n}-1}{r}](1+r)\\\\FVx=X[\frac{(1.07)^{14}-1}{0.07}](1.07)*1.07^{28}\\FVx=220.4038x$

For Y,n=10,r=7%

Therefore:-

$FVy=Y[\frac{(1+r)^n-1}{r}]\\FVy=Y[\frac{(1.07)^{10}-1}{0.07}]\\FVy=19.3430y\\X-Y=100\\220.4038X+19.3430Y=100000\\Y=X-100\\220.4038X-19.3430(X-100)=100000\\101934.3027=239.7468X\\X=425.17\\Y=325.17$