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

Fund X 311.87

Fund Y 172.41

Total at end of year two $559,46

Step-by-step explanation:

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

`X(1+0.08/4)^(10*4) + Y(1+0.06/2)^(10*2) = 1,000`

`X(1+0.08/4)^(5*4) = 2Y(1+0.06/2)^(5*2)`

we can solve the factor and solve for each variable:

`\left \{ {{2.20803966361485X + 1.80611123466941Y =1,000} \atop {1.48594739597835X =2Y*1.34391637934412}} \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*4) + Y(1+0.06/2)^(10*2) = 1,000`

`311.87(1+0.08/4)^(10*4) + 172.41(1+0.06/2)^(10*2) = 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*4) + 172.41(1+0.06/2)^(2*2) = Amount`

Amount = 365.41 + 194.05 = 559,46