Question

1. If you want to have an $500,000 amount (F) when you retire in 35 years, what equal series amount (A) do you need to invest each year with a 5% interest rate? (Hint, use (^{A/F, i, n}))

2. Same question as 1, but how much is the equal series amount (A) if you had procrastinated for 10 years and now have only 25 years to accumulate the $500,000 desired at retirement?

3. Same question as 2, but the interest rate is 7%, what equal-series amount (A) do you need to invest over 25 years to accumulate the $500,000 desired at retirement?

Answer 1

If you want to have an $500,000 amount (F) when you retire in 35 years, what equal series amount (A) do you need to invest each year with a 5% interest rate? (Hint, use (A/F, i, n))

We can use Future Value of an Annuity formula to calculate the equal amount of annual investments (A) by you

F = A *{(1+i) ^n−1} / i

Where,

Future value of annual investments (F) = $500,000

A = Annual investments or equal series amount =?

n = N = number of payments = 35 years

i = I/Y = interest rate per year =5%

Therefore,

$500,000 = A *{(1+5%) ^35−1} /5%

A = $5,535.85

Therefore you have to invest $5,535.85 per year to achieve your retirement goal.

Same question as 1, but how much is the equal series amount (A) if you had procrastinated for 10 years and now have only 25 years to accumulate the $500,000 desired at retirement?

Again we can use Future Value of an Annuity formula to calculate the equal amount of annual investments (A) by you

F = A *{(1+i) ^n−1} / i

Where,

Future value of annual investments (F) = $500,000

A = Annual investments or equal series amount =?

n = N = number of payments = 35 - 10 = 25 years

i = I/Y = interest rate per year =5%

Therefore,

$500,000 = A *{(1+5%) ^25−1} /5%

A = $10,476.23

Now you have to invest $10,476.23 per year to achieve your retirement goal.

Same question as 2, but the interest rate is 7%, what equal-series amount (A) do you need to invest over 25 years to accumulate the $500,000 desired at retirement?

Again we can use Future Value of an Annuity formula to calculate the equal amount of annual investments (A) by you

F = A *{(1+i) ^n−1} / i

Where,

Future value of annual investments (F) = $500,000

A = Annual investments or equal series amount =?

n = N = number of payments = 35 - 10 = 25 years

i = I/Y = interest rate per year = 7%

Therefore,

$500,000 = A *{(1+7%) ^25−1} /7%

A = $7,905.26

Now you have to invest $7,905.26 per year to achieve your retirement goal.