Question

Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible

quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R.

Answer 1

Let X be the amount Mr Saver invests at t = 0.

The interest he earns during t = 0 to t = 1 can be expressed as:

Interest = X * R * (1/4)

The interest he earns during t = 0.5 to t = 1.5 can be expressed as:

Interest = X * R * (3/4)

Since the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1, we can set up the following equation:

X * R * (3/4) = 1.0816 * (X * R * (1/4))

Solving for R, we get:

R = 4.3264 Therefore, the exact value of R