Question

Santiago plans to save $20,000 per year until he retires. His first savings contribution to his Find PMT for PV annuity from FV annuity retirement account is expected in 1 year from today. Santiago plans to retire in 8 years from today, immediately after making his last $20,000 contribution to his retirement account. He then plans to be retired for 8 years. Santiago expects to earn 9.0 percent per year in his retirement account, both before and during his retirement. If Santiago receives equal annual payments from his retirement account during his retirement with the first of these annual retirement payments received in 1 year after he retires and the last of these annual retirement payments received in 8 years after he retires, then how much can Santiago expect each of his annual retirement payments to be?

Answer 1

Santiago can expect each of his annual retirement payments to be approximately $3,642.20. This calculation is based on his plan to save $20,000 per year for 8 years, with an expected 9.0% annual interest rate before and during retirement, following the annuity formula. The result reflects the present value of his annuity, adjusting for the time value of money and providing a reliable estimate for his future retirement income.

Step-by-step explanation:

Santiago's situation can be analyzed using the annuity formula for the present value of an annuity (PVA):

`\[ PVA = PMT * \left( ((1 - (1 + r)^(-n)))/(r) \right) \]`

`\( PVA \)` is the present value of the annuity,

`\( PMT \)` is the annual payment,

`\( r \)` is the interest rate per period,

`\( n \)` is the number of periods.

In Santiago's case,
`\( PVA \)` is the total amount he wants to save for retirement, which is $20,000 per year for 8 years, with an interest rate
`\( r \)` of 9%. Using these values, we can rearrange the formula to solve for
`\( PMT \)`:

`\[ PMT = (PVA)/(\left( ((1 - (1 + r)^(-n)))/(r) \right)) \]`

Substituting the given values:

`\[ PMT = (20000)/(\left( ((1 - (1 + 0.09)^(-8)))/(0.09) \right)) \]`

After performing the calculations, the annual payment
`\( PMT \)` is approximately $3,642.20.

This means that Santiago can expect to receive an annual retirement payment of around $3,642.20 for each of the 8 years after he retires. This calculation considers the time value of money, ensuring that the future value of his savings is adjusted for the expected interest earned on his retirement account.