Question

You would like to have the current equivalent in terms of today's buying power of $4,000 in years 10 11 and 12 How much would you have to invest in years 1, 2 and 3 (the same amount in each year in nominal terms) to fund this level of real consumption? You expect inflation to be 3% per year over that time period. Your investments earn 7% per year in nominal terms.

Answer 1

First let’s calculate the current equivalent amount in terms of today's buying power of $4,000 in years 10, where the inflation is 3% per year over that time period.

FV = PV *(1+ inflation rate) ^t

Where,

Equivalent amount in terms of today's buying power is future value FV=?

Present value PV = $4,000

Inflation rate = 3% per year

Time period t = 10 years

Therefore

FV for year 10 = $4,000 *(1+3%) ^10

= $5,375.67

Therefore we need amount $5,375.67 after 10 years which in equivalent of today's buying power of $4,000.

Now we have to discount amount $5,375.67 at discount rate of 7% to calculate its present value

PV = FV/ (1+discount rate) ^t

PV = $5,375.67/ (1+7%) ^10

PV1 = $2,732.72

Similarly we can calculate the amount for years 11 and years 12 in following manner

FV for year 11= $4,000 *(1+3%) ^11

= $5,536.94

And PV =$5,536.94 / (1+7%) ^11

PV2 = $2,630.56

FV for year 12= $4,000 *(1+3%) ^12

= $5,703.04

And PV = $5,703.04/ (1+7%) ^12

PV3 = $2,532.22

Now after adding all three present values, we get the total amount

Total PV = $2,732.72 +$2,630.56 +$2,532.22 = $7,895.50

We can use following Present Value of an Annuity formula to calculate the annual investment amount for year 1, 2 and 3 at 7% interest rate

PV of amount = PMT * [1-(1+i) ^-t)]/i

Where,

Present value of total amount (PV) = $7,895.50

The annual investment PMT =?

Number of payments t = 3 (years)

Annual interest rate I =7%

Therefore

$7,895.50= PMT * [1- (1+7%) ^-3]/7%

Or PMT = $3,008.59

Therefore we have to invest amount $3,008.59 in years 1, 2 and 3 to fund this level of real consumption.