Question

Bonnie wants to save money to meet three objectives. First, she would like to be able to retire 30 years from now with retirement income of $26,000 per month for 30 years, with the first payment received 30 years and 1 month from now. Second, she would like to purchase a cabin in Vancouver in 10 years at an estimated cost of $228,000. Third, after she passes on at the end of the 30 years of withdrawals, he would like to leave an inheritance of $700,000 to her daughter Natalie. Bonnie can afford to save $1,500 per month for the next 10 years.

  

If Bonnie can earn a 9 percent EAR before she retires and a 6 percent EAR after she retires, how much will she have to save each month in Years 11 through 30?

Answer 1

Bonnie can afford to save $1,500 per month for the next 10 years.

10 years = 120 months

As a first step we need to convert EAR to APR

EAR Before she retires = 9%

EAR = ((1+APR/n)^n) -1

.09 = ((1+APR/12)^12) – 1

APR = 8.6%

Monthly rate = 8.6 / 12 = 0.72%

EAR after she retires = 6%

APR = 5.8%

Monthly rate = 0.48%

Using the financial Calculator,

PMT = 1500

N= 120 months

Rate = 0.72%

Calculate future value, FV = $284,437.30

So, at the end of 10^th year she will have $2,84,437.30. She can purchase a cabin for $228,000

Amount she will have after the purchase = $284,437.30 - $228,000 = $56,437.30

She decided to leave inheritance of $700,000

Retirement income = $26,000

Next we need to find the present value of money she must have at the end of 30 years (i.e at the time of retirement) in order to leave an inheritance of $700,000

Using financial Calculator,

PMT = 26,000

FV = 700,000

N = 30 * 12 = 360 months

Rate = 0.48%

Calculate PV, PV = $45,75,330.26

The amount he must save in the year 11 through 30.

Take the PV amount we have calculated in the previous step as FV. FV = $45,75,330.26

she is having $56,437.30 at the end of 10^th year. So, PV = $56,437.30

N = 20 * 12 = 240 months (year 11 through 30)

Rate = 0.72%

Find PMT, PMT = $6,674.95 ≈ $6,675

She has to save $6,675 every month in years 11 through 30.