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

Y=$325.17

Step-by-step explanation:

Both X and Y are annuity due payments.

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

Therefore

`FVx=X[((1+r)^(n)-1)/(r)](1+r)\\\\FVx=X[((1.07)^(14)-1)/(0.07)](1.07)*1.07^(28)\\FVx=220.4038x`

For Y,n=10,r=7%

Therefore:-

`FVy=Y[((1+r)^n-1)/(r)]\\FVy=Y[((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`