. A firm is planning to invest enough each year to repay £100 million debt that is due in 6 years. If the relevant rate of interest is 4% pa, how much must be invested at the end of each year for the next 6 years?

To solve this problem, we need to use the formula for the future value of an ordinary annuity. An ordinary annuity is a sequence of equal payments made at the end of each period over a certain amount of time. The formula is:

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

where: FV = future value of the annuity (the total amount of money accumulated after n years) P = payment per period (the amount of money invested at the end of each year) r = interest rate per period (in this case, the annual interest rate) n = number of periods (the number of years)

We know that FV = £100 million, r = 4% = 0.04, and n = 6 years. We want to find P. So we rearrange the formula to solve for P:

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

Substituting the known values:

P = £100 million * 0.04 / [(1 + 0.04)^6 - 1]

Now, calculate the expression in the brackets:

(1 + 0.04)^6 - 1 = 1.2653 - 1 = 0.2653

Then, substitute this value back into the formula:

P = £100 million * 0.04 / 0.2653

Finally, calculate the value of P:

P = £15.07 million

So, the firm must invest £15.07 million at the end of each year for the next 6 years to repay the £100 million debt.