Deposits to Accumulate a Future Sum
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 required 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 = 30,000, N = 5, I/Y = 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.
Loan Amortization
Question number 2, loan amortization.
You borrow $6,000 at 10 percent and agree to make equal annual end-of-year payments over 4 years.
To find the size of the payments, the lender determines the amount of a 4-year
annuity discounted at 10 percent 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 = 6,000, N = 4, I/Y = 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 one principal balance will be carried forward to Year 2 beginning of year principal.
Monthly Housing Loan Payment
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 = 100,000, I/Y = 7%, N = 30 times 12 = 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.
Growth Rates
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 compounding
period, N, it is only 4, although it has 5 years. Because, the cash flows only grow four times.
Using financial calculator, set annually compounding, and set end mode. Then key in,
PV = 1,250, FV = negative 1,520, N = 4. Last step press Rate, you will get the growth rate, 5.01%.
interest rate
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 = 2,000, PMT = negative 514.14, N = 5.
Last step press Rate, you will get the loan interest rate, 9%.
Finding an Unknown Number of Periods
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
= negative 1,000, FV = 2,500, I/Y = 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.
Retirement Fund
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,
PMT = negative 400, I/Y = 12%, N = 30 times 12 = 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.
