Question

Retirement Planning. A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year.

b. How would the answer to part (a) change if the couple also realize that in 20 years, they will need to spend $60,000 on their child’s college education?

Answer 1

The problem is based upon the concept of time value of money which says that the money received today worth more than the money received in future. The investment made on regular basis is known as annuity. Whereas, the amount invested once is known as the lump sum investment.

The formula to compute the future value of annuity payment is provided below.

…… (1)

Where,

The monthly payment is C.

The future value is FV.

Periodic interest rate is i.

Number of payments is n.

The formula to calculate the Present Value of annuity is provided below.

…… (2)

Where,

The monthly payment is C.

The present value is PV.

Periodic interest rate is i.

Number of payments is n.

The formula to compute the future value of one time deposit is provided below.

…… (3)

Where,

The present value is PV.

Periodic interest rate is i.

Number of payments is n.

The future value is FV.

For the given problem requirement is to compute the amount of annual deposit to accumulate fund for retirement.

The following given information will be used to compute the amount of annual deposit to accumulate fund for retirement.

Rate of interest is 8%.

Retirement period is 25 years.

Saving period is 50 years.

Amount of withdrawal in retirement period is $30,000.

(a)

Compute the amount of annual savings in the following steps:

First step: Compute the amount of retirement fund to withdraw $30,000 in each year of retirement using equation (2) as follows:

Hence, the required amount of retirement fund is.

Second step: Compute the amount of annual savings to accumulate fund for retirement using equation (1) as follows:

Thus, the required amount of annual savings is.

(b)

The couple wants to spend $60,000 to their children’s college education in 20-years which is 30-years earlier of retirement. Thus, additional amount should be saved in each year of saving period to meet this requirement.

Compute the amount of annual savings in the following steps:

First step: Compute the future value of education expense at the time of retirement using equation (3) as follows:

Thus, the amount of retirement fund will increase by.

Second step: Compute the amount of annual savings to accumulate fund for retirement using equation (1) as follows:

Thus, the required amount of annual savings is.