Question

You are given:

(i.) Fund A accumulates at a nominal interest rate of 9% convertible monthly.

(ii.) Fund B accumulates at a nominal discount rate of 12% convertible semi-annually.

(iii.) At the end of 5 years, the total amount in the two funds is 1000.

(iv.) At the end of 2 years, the amount in Fund A equals the amount in Fund B.

Let X be the initial amount in Fund A and Y the initial amount in Fund B. Determine X Y

Answer 1

As per question let,

Initial amount in fund A = X

Initial amount in fund B = Y

Now,

1. At the end of Year 5,

Total Amount in 2 Funds = 1000

Therefore,

[where,

R1= Nominal rate of Interest of Fund A

R2= Nominal rate of Interest of Fund B

n= Number of Years]

(using calculator)

...........Equation 1

2. At the end of Year 2

amount in fund A = amount in fund B

..... Equation 2

Substituting Value of Y in equation 1

.....using value of X in Equation 2

Hence,

Initial amount in fund A = X = 306.484

Initial amount in fund B = Y = 290.446