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You want to receive $5000 per month for 20 years in real dollars in an account when you retire in 35 years. The first monthly payment to be received 1 month after you retire. The nominal return on your investment is 9.94 percent and the inflation rate is 3.2 percent. What is the real amount you must deposit each year for 35 years to achieve your goal

Sagot :

Hyderali230idn

Answer:

The real amount you must deposit each year for 35 years to achieve your goal is $5,359.02

Explanation:

To calculate the real amount we need to calculate the real interest rate as follow

1 + Nominal rate = ( 1 + Real rate ) x ( 1 + Inflation rate )

1 + 9.94% = ( 1 + Real rate ) x ( 1 + 3.2% )

1.0994 = ( 1 + Real rate ) x 1.032

1 + Real rate = 1.0994 / 1.032

1 + Real rate = 1.06531

Real rate = 1.06531 - 1

Real rate = 0.06531

Real rate = 6.531% = 6.53%

We need to calculate the PV of the payment that should be received.

Use the following formula to calculate the present value

PV of Annuity = Annuity payment x ( 1 - ( 1 + Interest rate )^-numbers of annuity payments ) / Interest rate

Where

Annuity Payment = $5,000 per month

Interest rate = 6.53% / 12 = 0.5442%

Numbers pf annuity payments = 20 years  x 12  payments per year = 240 payment

PLacing values in the formula

PV of Annuity = $5,000 x ( 1 - ( 1 + 0.5442% )^-240 ) / 0.5442%

PV of Annuity = $5,000 x 133.80362

PV of Annuity = $669,018.09

Now calculate the amount of deposit required to receive the payment after retirement.

Use the following formula to calculate the real deposit

Future value of annuity = Annuity Payment x ( 1 + Interest rate )^numbers of annuity payments - 1 ) / Interest rate

Where

Future value of annuity = $669,018.09

Interst rate = 6.53%

Numbers of annuity payment = 35 years x 1 payment per year = 35 payments

Annuity payment = Real amount of deposit = ?

Placing values in the formula

$669,018.09 = Real amount of deposit x ( 1 + 6.53% )^35 - 1 ) / 6.53%

$669,018.09 = Real amount of deposit x 124.83967

Real amount of deposit = $669,018.09 / 124.83967

Real amount of deposit = $5,359.02

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