Emma requires a pension of €10,000 per annum starting in 10 years' time. If the annuity rate applying in 10 years' time for the type of pension she wants will be 4%, what lump sum does she need to invest now to make up that pension in 10 years' time, assuming her investment can earn a return of 5% per annum compound over that period?

• A. €186,000
• B. €153,500
• C. €195,250
• D. €201,250

Answer: (B)

This problem combines two small steps: first, figure out how much money is needed at the start of the pension to produce €10,000 every year given the future annuity rate; second, discount that amount back to today using the expected investment return.

At 10 years’ time, to generate €10,000 per year with an annuity rate of 4%, you’d need capital of 10,000 ÷ 0.04 = €250,000.

To have €250,000 in 10 years starting from now, with an annual return of 5% compounded, the present value is 250,000 ÷ (1.05)^10. Since (1.05)^10 ≈ 1.6289, the present value is about 250,000 ÷ 1.6289 ≈ €153,500.

So, the lump sum to invest now is approximately €153,500.