Question

You want to have $2.5 million in real dollars (HINT: it means we need to use the real interest rate in the calculation) in an account when you retire in 40 years. The nominal return on your investment is 10.3% and the inflation rate is 3.7% (HINT: do not use the approximation when finding the real interest rate). What real amount must you deposit each year to achieve your goal?

Can anyone solve this without using excel formulas? Thanks!

Answer 1

The amount is computed as follows:

Future value = Annual deposits x [ [ (1 + r)ⁿ – 1 ] / r ]

r is computed as follows:

= [ (1 + nominal rate) / (1 + inflation rate) ] - 1

= [ (1 + 0.103) / (1 + 0.037) ] - 1

= [ 1.103 / 1.037 ] - 1

= 0.06364513

So, the amount will be as follows:

$ 2,500,000 = Annual deposits x [ [ (1 + 0.06364513)⁴⁰ - 1 ] / 0.06364513 ]

$ 2,500,000 = Annual deposits x 169.685887

Annual deposits = $ 2,500,000 / 169.685887

Annual deposits = $ 14,733.11 Approximately