Question

Consider the following data:
 Account A earns 8% nominal quarterly interest.
 Account B earns 6% convertible interest twice a year.
 At the end of 5 years the amount in account A is twice the amount in account B.
 At the end of 10 years the sum of the accumulated amount in both accounts is $ 1,000
Analytically compute  the sum of the accumulated amount in both accounts at the end of 2 years.

Answer 1

Let the initial amount in Account A be A and in Account B be B

Future Value=Present Value*(1+r/m)^(m*t)

At the end of 5 years
Amount in Account A=A*(1+8%/4)^(4*5)
Amount in Account B=B*(1+6%/2)^(2*5)

Amount in Account A is twice the amount in Account B
Hence,
A*(1+8%/4)^(4*5)=2*B*(1+6%/2)^(2*5)

At the end of 10 years
Amount in Account A=A*(1+8%/4)^(4*10)
Amount in Account B=B*(1+6%/2)^(2*10)

Amount in Account A+Amount in Account B=1000
=>A*(1+8%/4)^(4*10)+B*(1+6%/2)^(2*10)=1000

Solving the two equations simultaneously we get
A=311.86
and B=172.41

Sum of amount in 2 years=311.86*(1+8%/4)^(4*2)+172.41*(1+6%/2)^(2*2)=559.442668