Question

In: Finance

You want to have $1.05 million in real dollars in an account when you retire in...

You want to have $1.05 million in real dollars in an account when you retire in 38 years. The nominal return on your investment is 8 percent and the inflation rate is 1.5 percent. What is the real amount you must deposit each year to achieve your goal?

A. $10,667.67

B. $10,878.49

C. $11,194.39

D. $11,302.03

E. $11,744.12

Expert Solution

Step-1, Calculation of Real Rate of Return

Real Rate of Return = [(1 + Nominal Rate) / (1 + Inflation Rate)] – 1

Nominal Rate = 8%

Inflation Rate = 1.50%

Real Rate of Return = [(1 + Nominal Rate) / (1 + Inflation Rate)] – 1

= [(1 + 0.08) / (1 + 0.0150)] – 1

= 1.06403941 – 1

= 0.06403941 or

= 6.403941%

Step-2, Calculation of amount to be deposited each year to achieve the goal

Future Value of an ordinary annuity is calculated by using the following formula

Future Value of Annuity = P x [{(1+ r) ⁿ - 1} / r]

Future Value = $10,50,000

Number of periods (n) = 38 Years

Annual Interest rate = 6.403941%

Annual Deposit (P) = ?

Future Value of Annuity = P x [{(1+ r) ⁿ - 1} / r]

$10,50,000 = P x [(1 + 0.06403941)³⁸ - 1} / 0.06403941]

$10,50,000 = P x [(10.577745 – 1) / 0.06403941]

$35,00,000 = P x [9.577745 / 0.06403941]

$10,50,000 = P x 149.560176

P = $10,50,000 / 149.560176

P = $7,020.59 per year

“Therefore, the real amount that must be deposited each year to achieve the goal = $7,020.59 per year”

Hii… The real amount that must be deposited each year to achieve the goal of $1.05 Million in 38 years is $7,020.59 per year, but this answer choice is not given in the question….Can you please confirm the same….!!!

jeff jeffy answered 1 year ago

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