Question

In: Finance

Suppose you and your husband have decided that when you retire in 15 years you want...

Suppose you and your husband have decided that when you retire in 15 years you want to take a trip around the world for a year. You realize that you need to begin saving now for this trip of a lifetime. You want to be able to deposit annually (end of year payments) a fixed amount in an interest bearing account. It is estimated that monthly after that you will need to withdraw $5000 monthly for spending money. You will make the down payment at year 15 and the monthly payments will begin the first month after year 15 and will go for 12 months. How much must you deposit annually to be able to pay for these expenses. Assume 6% interest annual rate with monthly compounding.

Expert Solution

First we will Calculate the downpayment needed at year 15

Monthly withdrawls after year 15 = $5000, Annual interest rate = 6% with monthly compounding

Monthly rate = Annual interest rate with monthly compounding / 12 = 6% / 12 = 0.50%

No of withdrawls or months = 12

Here Monthly withdrawls form an ordinary annuity. Downpayment at year 15 will equal to present value of monthly withdrawls for 12 months.

We can find the present value of monthly withdrawls or downpayment at year 15 using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get Downpayment at year 15 = $58094.6603

Now we will calculate the amount(end of year) needed to deposit per year

Since the interest rate is compounded monthly, annual deposits will earn interest at effective annual rate

Effective annual rate = (1+ monthly rate)¹² - 1 =(1+0.50%)¹² - 1 = 1.061677 - 1 = 0.061677 = 6.1677%

We can find the amount needed to deposit each year using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,pv,-fv)

In the formula pv = 0 as there is no initial lumpsum deposit

Using PMT function in excel, we get Annual deposit at end of year = 2464.3855 = 2464.39 (rounded to two decimal places)

Amount to be deposited annually to pay for expenses = $2464.39

jeff jeffy answered 1 month ago

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