Question

Nelson Collins decided to retire to Canada in 10 years. What amount should he deposit so that he will be able to withdraw $80,000 at the end of each year for 25 years after he retires. Assume he can invest 7% interest compounded annually.

Answer 1

$1,016,699

Step-by-step explanation

The amount, A that an invested sum of P, becomes over time t, at a rate of r% is given as

A = P (1 + r)ᵗ

For this question,

A = Total amount that the amount invested becomes = $80,000 × 25 = $2,000,000

P = Amount invested at the start of the 10 years before retirement = ?

r = 7% = 0.07

t = 10 years

A = P (1 + r)ᵗ

2,000,000 = P (1 + 0.07)¹⁰

2,000,000 = P (1.07)¹⁰

Note that 1.07¹⁰ = 1.967

2,000,000 = 1.967P

We can rewrite this as

1.967P = 2,000,000

Divide both sides by 1.967

(1.967P/1.967) = (2,000,000/1.967)

P = $1,016,699

Hope this Helps!!!