Hi, i was wondering if someone could please help me with these 3 finance questions. it would be must appreciated
1. you receive payments of 1000 dollars every 8 montsh for the next 9 years. the first payment will occur 8 months from today. there will be a total of 12 payments. what is the present value of this investment. the required rate of return is 10% compounded annually.
2. you are surprised to learn that your mom bought a new car today. she has to make 48 monthly payments of 800$, and the first payment is due today. if the interst rate is 7% compounded quarterly, what is the price of the car?
3. your sister wants to purchase an investment that will pay her 500$ every 3 months for the next 10 yrs. the first payment will be made 3 months from today. If your sister requires a rate of return of 8% compounded monthly what should she expect to pay for the investment?
thanks
1. If the no of level investments be ‘t’, total no of level instalments be ‘n’ and total charge for
credit be ‘c’ then the interest rebate is given by…………………………………………
2.
Of course, I'll be happy to help you with these finance questions. Let's solve each question step by step.
1. To find the present value of the investment, we can use the Present Value of Annuity formula. The formula is:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
PMT = Payment amount per period
r = Rate of return per period
n = Total number of periods
In this case, the payment amount per period is $1000, the rate of return is 10% compounded annually, and the total number of periods is 12. However, the payments are made every 8 months, so we need to adjust the rate and number of periods accordingly.
The first step is to convert the annual rate of return to the rate per period. Since the payments are made every 8 months, we divide the annual rate by 3 (as there are 3 payments per year) and convert it to a decimal: 10% / 3 = 0.0333.
Next, we need to determine the number of periods. Since the payments are made every 8 months for a total of 9 years, we multiply the number of years by the number of payments per year: 9 years * 3 payments/year = 27 periods.
Now we can plug in the values into the formula:
PV = $1000 * [1 - (1 + 0.0333)^(-27)] / 0.0333
Simplifying the equation will give you the present value of the investment.
2. To determine the price of the car, we'll use the Present Value of Annuity formula again, but with some modifications. The formula remains the same, but we need to adjust the values based on the given information.
The payment amount per period is $800, the interest rate is 7% compounded quarterly, and there are 48 monthly payments. We need to convert the interest rate to the rate per quarter by dividing the annual rate by 4: 7% / 4 = 0.0175.
Next, we need to adjust the total number of periods. Since the payments are made monthly for 48 months, the total number of periods remains unchanged.
Plugging in the values into the formula:
PV = $800 * [1 - (1 + 0.0175)^(-48)] / 0.0175
Simplify the equation to find the price of the car.
3. Once again, we'll use the Present Value of Annuity formula to determine the price of the investment. The payment amount per period is $500, the rate of return is 8% compounded monthly, and there are 10 years of payments.
We need to convert the annual rate of return to the rate per period. Since the payments are made every 3 months, we divide the annual rate by 12 (as there are 12 payments per year) and convert it to a decimal: 8% / 12 = 0.0067.
Next, we determine the number of periods. Since the payments are made every 3 months for a total of 10 years, we multiply the number of years by the number of payments per year: 10 years * 4 payments/year = 40 periods.
Plugging in the values into the formula:
PV = $500 * [1 - (1 + 0.0067)^(-40)] / 0.0067
Simplify the equation to find the price of the investment.
Remember to simplify the equations and input the values correctly to get accurate answers. Let me know if you have any further questions!