A payment of $10 is made on 31st December of each year from 2001 to 2012. Force of interest is 8% p.a.What is the value of all payments accumulated on 31 December 2013?

To solve this problem, we need to understand the concept of compound interest and the formula for the future value of an annuity.

An annuity is a series of equal payments made at regular intervals. In this case, the annuity is $10 paid annually from 2001 to 2012.

The formula for the future value of an annuity is:

FV = P * [(1 + r)^n - 1] / r

where: FV = future value of the annuity P = payment per period (in this case, $10 per year) r = interest rate per period (in this case, 8% per year, or 0.08) n = number of periods (in this case, 12 years)

However, since the last payment is made at the end of 2012 and we want to know the value on 31 December 2013, we need to account for one more year of interest on the total amount.

So, the calculation would be:

Step 1: Calculate the future value of the annuity at the end of 2012:

FV = $10 * [(1 + 0.08)^12 - 1] / 0.08 =$165.30

Step 2: Calculate the value of this amount one year later (at the end of 2013):

FV_2013 = $165.30 * (1 + 0.08) =$178.52

So, the value of all payments accumulated on 31 December 2013 is $178.52.