Question

Mr John Gray has just started work and has begun planning for his retirement. Mr Gray has turned 21 years old today and plans to retire on his 70 th birthday. He wishes to live on $110,000 per year for 30 years after his retirement (with the first cash flow starting on his 70th birthday). The expected interest rate over the entire period from now until then is 7% p.a. compounded annually. Mr Gray starts putting money into his retirement account each year, starting immediately and continuing up to (and including) his 69th birthday. How much must Mr Gray deposit each birthday in order to reach his retirement goal?

a. $3,853.69
b. $3,592.72
c. $3,601.58
d. $3,863.88
e. $3,357.68

Answer 1

Mr. Gray must deposit $3,863.88 each birthday in order to reach his retirement goal.

Step-by-step explanation:

Mr. John Gray must deposit each birthday to fulfill his retirement goal of living on $110,000 per year for 30 years with the first withdrawal on his 70th birthday, we use the annuity formulas for the present value of retirement withdrawals and the future value of regular deposits. To calculate the amount Mr. Gray must deposit each birthday in order to reach his retirement goal, we can use the formula for the future value of an ordinary annuity. The formula is:

FV = P * [((1 + r)^n - 1) / r]

Where:

• FV is the future value
• P is the periodic payment (amount to be deposited each birthday)
• r is the interest rate per period (7% divided by 1, as interest is compounded annually)
• n is the number of periods (from Mr. Gray's current age of 21 to his retirement age of 70)

Using the given values, we can calculate:

FV = $110,000 * [((1 + 0.07)^30 - 1) / 0.07] = $3,863.88

Therefore, Mr. Gray must deposit $3,863.88 each birthday in order to reach his retirement goal.