John is 30 years old. He comes up with a plan to save for his retirement at 65 years. Currently, he has saved $20,000 in a balanced superannuation account earning 5.1% p.a. compounded annually. He has set himself a retirement target of $2,000,000. How much must be deposited every year into John's superannuation account, starting next year, to reach his target? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Question
John is 30 years old. He comes up with a plan to save for his retirement at 65 years. Currently, he has saved 2,000,000. How much must be deposited every year into John's superannuation account, starting next year, to reach his target? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
To solve this problem, we need to use the formula for the future value of a series of payments or annuities compounded annually, which is:
FV = P * [(1 + r)^n - 1] / r
where: FV is the future value of the series of payments (the retirement target), P is the amount of each payment (the amount John needs to deposit each year), r is the interest rate per period (annual interest rate), n is the number of periods (number of years until retirement).
We know that FV = 20,000 in his account. The future value of this amount in 35 years is:
FV_existing = PV * (1 + r)^n = 150,813.26
So, the future value of the series of payments must be 150,813.26 = $1,849,186.74.
Substituting FV, r, and n into the formula, we get:
$1,849,186.74 = P * [(1 + 0.051)^35 - 1] / 0.051
Solving for P gives:
P = 11,286.57
So, John must deposit approximately $11,286.57 into his superannuation account each year to reach his retirement target.
Similar Questions
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