Hey guys, I am Derek, welcome to my channel. In this video, we are gonna discuss some application questions of time value of money. Question number 1, deposits to accumulate a future sum.
Suppose you want to buy a house 5 years from now, and you estimate that the down payment needed will be $30,000. How much would you need to deposit at the end of each year for the next 5 years to accumulate $30,000? if you can earn 6% on your deposits? For this question, the down payment $30,000 is the money that you need after 5 years, so it is FV. Using financial calculator, set annually compounding and set end mode.
Then key in FV equals 30,000, N equals 5, IY equals 6. Last step, press PMT, you will get the answer. Negative PMT means this is the money that you will have to pay every year. Question number two, loan amortization. You borrow $6,000 at 10% and agree to make equal annual end-of-year payments over four years. To find the size of the payments, the lender determines the amount of a four-year annuity discounted at 10% that has a present value of $6,000.
For this question, loan amount $6,000 is the money that you will receive now, so it is PV. Using financial calculator, set annually compounding and set end mode. Then key in PV equals 6000, N equals 4, IY equals 10. Last step, press PMT, you will get the answer.
Negative PMT means, this is the loan payment that you will have to pay every year. This table is a sample of a loan amortization schedule. Loan payment will be the same for every year. Interest is calculated based on the beginning of year principal times 10%.
Principal payment can be calculated by taking the loan payment minus interest. For end-of-year principal, it is calculated by taking the beginning of year principal minus principal. Year 1 principal balance will be carried forward to year 2 beginning of year principal. Question number 3. Monthly housing loan payment. If you borrow $100,000 at 7% fixed interest for 30 years in order to buy a house, what will be your monthly housing loan payment?
For this question, loan amount $100,000 is the money that you will receive now, so, it is PV. Please take note, this is a monthly compounding question. Using financial calculator, set monthly compounding and set end mode.
Then key in, PV equals 100,000. IY equals 7%, N equals 30 times 12 is equal to 360. Last step press PMT, you will get the answer. Negative PMT means this is the loan payment that you will have to pay every month.
Question number 4, growth rates. You wish to find the growth rates reflected in the stream of cash flows that you received from a real estate investment over the period from 2018 through 2022, as shown above. For this type of question, you will need to set the first year as PV, last year as FV. One should be positive, the other one should be negative.
So, I'll set PV as positive, FV as negative. About the compounding period, N, it is only 4, although it has 5 years. Because, the cash flows only grow 4 times.
Using financial calculator, set annually compounding, and set end mode. Then key in PV equals 1250, FV equals negative 1520, N equals 4. Last step, press rate, you will get the growth rate 5.01%. Question number 5, interest rate.
You can borrow $2,000 to be repaid in equal annual end-of-year amounts of $514.14 for the next 5 years. Find the interest rate on this loan. Using financial calculator, set annually compounding and set end mode.
Then key in PV equals 2000, PMT equals negative 514.14 and equals 5. Last step, press rate, you will get the loan interest rate 9%. Question number 6, finding an unknown number of periods. You wish to determine the number of years it will take for your initial $1,000 deposit, earning 8% annual interest. to grow to equal $2,500. Simply stated, at an 8% annual rate of interest, how many years will it take for your $1,000 to grow to $2,500?
Using financial calculator, set annually compounding and set end mode. Then key in PV equals negative 1000, FV equals 2500, IY equals 8%. Last step, press periods. You will get 11.91. This means it will take about 12 years to grow your money from $1,000 to $2,500 based on 8% interest rate.
Question number 7, retirement fund. After graduation, you plan to invest $400 per month in the stock market. If you can earn 12% per year on your stocks, how much will you have accumulated when you retire in 30 years'time?
Using Financial Calculator, set Monthly Compounding and set End Mode. Then key in, PNT equals negative 400, IY equals 12%, N equals 30 times 12 is equal to 360. Last step, press FV. you will get the answer.
This is the sum of money that you will have accumulated after 30 years'time. Question number 8. Retirement fund for specific purpose. Upon retirement, your goal is to spend 5 years traveling around the world. To travel in style will require $250,000 per year at the beginning of each year.
If you plan to retire in 30 years, what are the equal monthly payments necessary to achieve this goal? The funds in your retirement account will compound at 10% annually. To better analyze this question, you'll need to draw a timeline. As shown here, before year 30, you'll be working and saving money.
On year 30, when you retire, you will start traveling around the world. In order for you to have that amount of money to travel, you need to save first. A very important idea here, your FV of saving must be equal to the PV of spending.
So, what you spend is what you saved. Go to the first step to get the PV of spending. Using financial calculator, set annually compounding and set beginning mode. Then key in PMT equals negative 250,000 and equals 5, IY equals 10. Last step, press PV, you will get 1.042 million dollars.
This is the PV of spending and also the FV of saving. So, we may set the same amount of money as FV in the next step. Using financial calculator, set monthly compounding and set end mode.
Then key in FV equals 1.042 million and equals 30 times 12 is equal to 360, IY equals 10. Last step, press PMT, you will get the final answer. This is the amount of money that you have to save every month in order to achieve your goal after retirement. So, around $460 monthly saving, it seems to be achievable. Last question, savings for specific purpose.
You plan to start pursuing master's degree 5 years from now. You'll have to pay tuition fee at the beginning of every 3 months for $3,000. Your study will take 2 and a half years to complete.
If you start depositing money into your bank account every month, how much should you deposit monthly? Assume an interest rate of 6% applied. We hold the same principle, FV of saving equals to PV of spending. So, what you spend is what you saved. Go to the first step to get the PV of spending.
Using financial calculator, set quarterly compounding and set beginning mode. Then key in, PMT equals negative 3000, IY equals 6, N equals 2.5 times 4 is equal to 10. Last step, press PV. You will get the answer, around $28,000.
This is the PV of spending, and also the FV of saving. So we may set the same amount of money as FV in the next step. Using financial calculator, now, set monthly compounding, and set end mode. Then key in, FV equals the PV that you just calculated, IY equals 6, N equals 5 times 12 is equal to 60. Last step, press PV. press PMT, you will get the final answer.
This is the amount of money that you have to save every month in order to achieve your goal for pursuing master's degree. Alright, that's all for this video. Thanks for watching.
See you in the next one. Bye.