Question

Suppose that you are now 30 and that you would like $2 million at age 65 to fund your retirement. You would like to save each year an amount that grows by 5% each year (that is, if you save $1 this year, you will save $1.05 next year). Assume that the discount rate is 8%. How much should you start saving at the end of this year

Answer 1

Answer:

$6,472.96

Explanation:

Data provided in the question:

Time for saving the money, n = 65 years - 30 years = 35 years

Future value of savings = $2 million = $2,000,000

Growth rate, g = 5% each year = 0.05

Discount rate, r = 8% = 0.08

Now,

Present value of $2 million will be calculated as

Future value = Present value × (1 + Discount rate )ⁿ

$2,000,000 = Present value × (1 + 0.08)³⁵

or

Present value = $135,269.08

Also,

Growing annuity is calculated using the formula

Present value = $\frac{A}{r-g}[1-(\frac{1+g}{1+r})^n]$

Here,

A is the first payment

therefore,

$135,269.08 = $\frac{A}{0.08-0.05}[1-(\frac{1+0.05}{1+0.08})^{35}]$

or

$135,269.08 × 0.03 = A × 0.6269

or

A = $6,472.96