Funding your retirement ??Emily Jacob is45 years old and has saved nothing for r
ID: 2618216 • Letter: F
Question
Funding your retirement??Emily Jacob is45 years old and has saved nothing for retirement.? Fortunately, she just inherited $76,000.Emily plans to put a large portion of that money into an investment account earning? a(n)10?% return. She will let the money accumulate for 2020 ?years, when she will be ready to retire. She would like to deposit enough money today so she could begin making withdrawals of ?$43,000 per year starting at age 66? (21 years from?now) and continuing for 24 additional? years, when she will make her last withdrawal at age 90. Whatever remains from her? inheritance, Emily will spend on a shopping spree. Emily will continue to earn 10?%on money in her investment account during her retirement? years, and she wants the balance of her retirement account to be? $0 after her withdrawal on her ninetieth birthday.
a. How much money must Emily set aside now to achieve that? goal? It may be helpful to construct a timeline to visualize the details of this problem.
b. Emily realizes that once she retires she will want to have less risky investments that will earn a slightly lower rate of? return,
9?% rather than 10?%. If Emily can earn 10?% on her investments from now until age? 65, but she earns just 9?% on her investments from age 65 to? 90, how much money does she need to set aside today to achieve her? goal?
c. Suppose Emily puts all of the?$76,000 that she inherited into the account earning10?%. As in part? b, she will earn only? a(n) 9?%
return on her investements after age 65. If Emily withdraws?$43,000 as planned on each birthday from age 65 to age? 90, how much will be left in her account for her heirs after her last? withdrawal?
a. The amount Emily must set aside now is ?$?. ?(Round to the nearest? cent.)b. The amount Emily needs to set aside to achieve her goal is ??.
?(Round to the nearest? cent.)c. The amount that will be left in the account for her heirs is
?. ?(Round to the nearest? cent.)
Explanation / Answer
Part 1)
Step 1: Calculate Total Amount Needed at Age 66
To determine the total amount needed at age 66, we need to calculate the present value of annual withdrawals that Emily plans to make from 66 year onwards. The present value of annual withdrawals can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value (if any).
Here, Rate = 10%, Nper = 25, PMT = $43,000 and FV = 0
Using these values in the above function/formula for PV, we get
Total Amount Needed at Age 66 = PV(10%,25,43000,0) = $390,312.72
____
Step 2: Calculate Present Value Today of Total Amount Needed at Age 66
We need to calculate the present value of total amount needed at 66 in order to determine the amount to be deposited today. The present value is arrived as below:
Present Value Today of Total Amount Needed at Age 66 (Amount to be Deposited Today) = Total Amount Needed at Age 66/(1+Interest Rate)^Years = 390,312.72/(1+10%)^21 = $52,743.18 (answer for Part 1)
____
Part 2)
Step 1: Calculate Total Amount Needed at Age 66
To determine the total amount needed at age 66, we need to calculate the present value of annual withdrawals that Emily plans to make from 66 year onwards. The present value of annual withdrawals can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value (if any).
Here, Rate = 9%, Nper = 25, PMT = $43,000 and FV = 0
Using these values in the above function/formula for PV, we get
Total Amount Needed at Age 66 = PV(9%,25,43000,0) = $422,370.92
____
Step 2: Calculate Present Value Today of Total Amount Needed at Age 66
We need to calculate the present value of total amount needed at 66 in order to determine the amount to be deposited today. The present value is arrived as below:
Present Value Today of Total Amount Needed at Age 66 (Amount to be Deposited Today) = Total Amount Needed at Age 66/(1+Interest Rate)^Years = 422,370.92/(1+10%)^21 = $57,075.22 (answer for Part 2)
____
Part 3)
Step 1: Calculate Future Value of $76,000 After 21 Years
The future value of $76,000 after 21 years is calculated as below:
Future Value of $76,000 = Amount*(1+Interest Rate)^Years = 76,000*(1+10%)^21 = $562,419
____
Step 2: Calculate Total Amount Needed at Age 66
To determine the total amount needed at age 66, we need to calculate the present value of annual withdrawals that Emily plans to make from 66 year onwards. The present value of annual withdrawals can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value (if any).
Here, Rate = 9%, Nper = 25, PMT = $43,000 and FV = 0
Using these values in the above function/formula for PV, we get
Total Amount Needed at Age 66 = PV(9%,25,43000,0) = $422,370.92
____
Step 3: Calculate Amount Left in the Account for Heirs
The total amount left in account for heirs is arrived as follows:
Total Amount Left in Account for Heirs = Future Value of $76,000 - Total Amount Needed at Age 66 = 562,419 - 422,370.92 = $140,048.08
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