High School

We appreciate your visit to Monali is 60 years old and considering retirement She is uncertain how long her lifelong savings will last which makes her hesitant She has saved. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Monali is 60 years old and considering retirement. She is uncertain how long her lifelong savings will last, which makes her hesitant. She has saved $70,000 and wishes to receive $600 a month for spending money. At an interest rate of 6%, compounded monthly, how many months will her money last?

A. 183 months
B. 176 months
C. 243 months
D. 173 months

Answer :

Monali's savings of $70,000, withdrawn at a rate of $600 per month with a 6% annual interest compounded monthly, will last approximately 173 months. The correct option is (d)

The question asks how long Monali's savings of $70,000 will last if she withdraws $600 per month with an interest rate of 6%, compounded monthly. To solve this, we can use the formula for the present value of an annuity because Monali's withdrawals form an annuity.

The formula for the present value of an annuity is:

[tex]PV = PMT * [(1 - (1 + r)^-n) / r][/tex]

Where:

  • PV is the present value of the annuity (the initial amount of savings)
  • PMT is the monthly payment amount (the withdrawal amount)
  • r is the monthly interest rate
  • n is the total number of payments (the number of months Monali's savings will last)

We are given:

  • PV = $70,000
  • PMT = $600
  • Annual interest rate = 6%, so the monthly interest rate r is 0.06/12

Now we just need to find 'n'. Rearranging the formula to solve for 'n' gives us:

n = [log(PMT / (PMT - r * PV)) / log(1 + r)]

Plugging in the given values:

n = [log(600 / (600 - (0.06/12) * 70000)) / log(1 + 0.06/12)]

Calculating 'n' gives us approximately 173 months before the savings are depleted.

Therefore, Monali's savings will last for 173 months. The correct option is (d)

Thanks for taking the time to read Monali is 60 years old and considering retirement She is uncertain how long her lifelong savings will last which makes her hesitant She has saved. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada