I am planning on retiring in exactly 12 years and want to celebrate retirement b

Question

I am planning on retiring in exactly 12 years and want to celebrate retirement by taking a trip to a variety of places. I want to have $120,000 available in 12 years to do so. To that end, I am going to start a savings account at a bank that offers an annual interest rate of 3.2%, with interest compounded quarterly. ALGEBRAICALLY SOLVE.

A.) Suppose that I want to make quarterly deposits for the next 10 years, and then cease making deposits. What should be deposited in the account each quarter so that the account balance will be at least $120,000 in 12 years?

B.) I recently sold a piece of property for $40,000. Suppose that I deposit that into the account right now, and also make quarterly deposits for the next 12 years. How much do I have to deposit each quarter so that I have at least $120,000 in the account in 12 years?

Explanation / Answer

I am planning on retiring in exactly 12 years and want to celebrate retirement by taking a trip to a variety of places. I want to have $120,000 available in 12 years to do so. To that end, I am going to start a savings account at a bank that offers an annual interest rate of 3.2%, with interest compounded quarterly. ALGEBRAICALLY SOLVE.

A.) Suppose that I want to make quarterly deposits for the next 10 years, and then cease making deposits. What should be deposited in the account each quarter so that the account balance will be at least $120,000 in 12 years?

Present Value of Future Value = 120000/(1+ 3.2/400)^(12*4) = $ 81,860.75

Quarterly Deposit Amount for 10 Year = pmt(rate,nper,pv,fv)

Quarterly Deposit Amount for 10 Year = pmt(3.2%/4, 40,-81860.75,0)

Quarterly Deposit Amount for 10 Year = $ 2399.50 or $ 2400

B.) I recently sold a piece of property for $40,000. Suppose that I deposit that into the account right now, and also make quarterly deposits for the next 12 years. How much do I have to deposit each quarter so that I have at least $120,000 in the account in 12 years?

Quarterly Deposit Amount for 12 Year = pmt(rate,nper,pv,fv)

Quarterly Deposit Amount for 12 Year = pmt(3.2%/4, 48,40000,-120000)

Quarterly Deposit Amount for 12 Year = $ 1053.67 or 1054

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