Answer to Question #187406 in Real Analysis for Angelo

Question

If the nominal interest rate is 3%, how much is P5,000 worth in 10 years in a continuous compounded account?

Answer 1

• The Nominal interest rate is 3%
• The time period of investment is 10 years
• Initial investment is P5000

We are given a continuous compounded account -This means that the initial investment of P5000 will earn interest continuously. The continuous rate of interest is the force of interest and is obtained from the Nominal rate of 0.03 as follows

Force of interest = ln(1 + 0.03)

where ln is the natural logarithm

=ln(1.03)

=0.02955880224154

To get the Accumulated amount after 10 years,Use the following Equation

Amount = Principal exp(10 × Force of interest)

Therefore

Amount = 5000exp(10×0.02955880224154)

= P6719.5819