Question

You are given:Fund X accumulates at an annual nominal interest rate of 8%, compounded quarterly.Fund Y accumulates at an annual nominal interest rate of 6%, compounded semiannually.At the end of 10 years, the total amount in the two funds combined is 1,000.At the end of 5 years, the amount in Fund X is twice that in Fund Y.Calculate the total amount in the two funds at the end of 2 years.

Answer 1

Answer:

Fund X 311.87

Fund Y 172.41

Total at end of year two $559,46

Explanation:

We will solve this like a math exercise with an equation system:

$X(1+0.08/4)^{10\times4} + Y(1+0.06/2)^{10\times2} = 1,000$

$X(1+0.08/4)^{5\times4} = 2Y(1+0.06/2)^{5\times2}$

we can solve the factor and solve for each variable:

$\left \{ {{2.20803966361485X + 1.80611123466941Y =1,000} \atop {1.48594739597835X =2Y\times1.34391637934412}} \right.$

On the second equation we clear for X

X = 1,808834394785938Y

Now we express this value on the first equation

2.20803966361485X + 1.80611123466941Y =1,000

2.20803966361485(1,808834394785938Y) + 1.80611123466941Y =1,000

And solve for Y

5.800Y = 1,000

Y = 172,413793103

And now we solve for X

X = 1,808834394785938 Y

X = 1,808834394785938 (172,413793103‬) = 311,867999

We can check if this is correct:

$X(1+0.08/4)^{10\times4} + Y(1+0.06/2)^{10\times2} = 1,000$

$311.87(1+0.08/4)^{10\times4} + 172.41(1+0.06/2)^{10\times2} = 1,000.01296786092$

We have 1 cent for rounding errors  so we could say we are okay.

Now we can proceed to calculate the total at the end of year two

$311.87(1+0.08/4)^{2\times4} + 172.41(1+0.06/2)^{2\times2} = Amount$

Amount =  365.41  +  194.05 = 559,46