49720 = Annuity (1/0.01 – 1/0.01(1.01)360)
49720 = Annuity (1/0.01 – 1/0.339)
=Annuity (100 -2.78)
= 97.22
511.42 for 30 YEARS
49720 = Annuity(1/0.01 – 1/0.01(1.01)180 )
=1/0.01 – 1/0.01(5.99)
=1/0.01 – 1/0.0599)
=(100 - 16.69)
596.87 for 15 years Answer: 85.46
Q3. You are trying to plan for retirement in 24 years and currently you have Rs63, 000.00 in a savings account and Rs24, 500.00 in stock. In addition you plan on adding to your savings by depositing Rs7, 000.00 per year in your SAVINGS account at the end of each of the next 10 years and then Rs19, 000.00 per year at the end of each year for the final 14 years until retirement. Assuming your savings account returns 8% compounded annually while your investment in stocks will return 2% compounded annually, how much will you have when you retire in 24 years? [Ignore taxes.]
Answer – 3
Given,
1. Present value of savings = Rs. 63,000
Rate of interest = 8% compounded annually
Time Period = 24 years
2. Present value of stock = Rs. 24,500
Rate of interest = 2% compounded annually
Time Period = 24 years
3. Present value = Rs. 7,000
Time Period = 10 years
4. Present value = Rs. 19,000
Time Period = 14 years
We will have to find the future value of the savings and stocks available now.
Solution:-
Formula: Future Value = Present Value (1+r/100) n
-
Future Value of savings = 63,000 (1+8/100)24
= 63,000 (1.08)24
= 63,000 * 6.34approx.
= Rs. 3, 99,494.38
-
Future Value of stocks = 24,500 (1+2/100) 24
= 24,500 (1.02) 24
= 24,500 * 1.608
= Rs. 39,396
-
Future value = 7000[(1.08)10-1/0.08]
= 7000 * 14.375
= Rs. 1,00,625
-
Future Value = 19000[(1.08)14-1/0.08]
= 19000 * 24.212
= Rs. 4,60,037.5
Now adding up all the four, we find out that when we retire after 24 years we are left with (Future Value), Rs. (3, 99,494.38+ 39,396+ 1,00,625+ 4,60,037.5) = Rs. 9,99,552.88
Q4. Suppose you buy a new Toyota for Rs15, 000.00, paying nothing down. You agree to a repayment schedule of sixty (60) equal monthly payments beginning one month from today. The banker's required return is 10% annually. How much will you owe on the car after 16 months?
Answer – 4
Given,
Present value of future annuity= Rs. 15,000
Interest= 0.0083
Time= 60 installments
We have to find out the annuity.
Solution:-
Present value of F.A. = Annuity [1/i-1/i (1+i)n ]
15,000=Annuity [1/0.0083-1/0.0083 (1.0083)60]
15,000=Annuity (1/0.0083-1/0.01362)
15,000=Annuity (120.48-73.42)
15,000=Annuity (47.06)
Annuity = 15,000/47.06
Annuity = Rs. 318.742
Q5. Brijesh, who recently sold his Scorpio, placed Rs16, 000.00 in a savings account paying annual compound interest of 7%. Calculate the amount of money that will have accrued if he leaves the money in the bank for 19 years.
Answer – 5
Given,
Present value of savings= Rs. 16,000
Rate of interest = 7%
Time period = 19 years
We need to find out the future value of the current savings.
Solution:-
Future value = present value (1+r/100)n
= 16,000(1+7/100)n
= 16,000(1.07)19
= 16,000(3.616)
Therefore, the Future Value of the current savings = Rs. 57,864.44
Q6. You need to have Rs18, 000.00 in 5 years. If money is placed into a savings account paying annual compound interest of 2%, how much money must be deposited today in order to have the required amount?
Answer – 6
Given,
Future value of the current saving = Rs.18,000
Time Period = 5 years
Rate of interest = 2%
We need to find out the money to be deposited today to get the required amount.
Solution:-
Future value=present value (1+r/100)n
-
18,000 = present value (1+2/100)5
-
18,000 = present value (1.02)5
- 18,000 = present value (1.104)
- Present value = 18,000/1.104
Therefore, the present value of the investment will be, Rs. 16,304.35
Q7. You are going to place Rs11, 000.00 in an investment paying compound interest of 16%, compounded monthly. Calculate the APY (Annual Percent Yield) on this investment?
Answer – 7
Given,
Rate of Interest = 16%
Present value of investment = Rs. 11000
Interest on monthly basis =16/12 =1.33
We have to find out the Annual Percent Yield.
Solution:-
Future Value = Present Value (1+r/100) n
= 11,000 (1+0.0133)12
=11,000 (1.1718)
Annual Percent Yield (APR) = Rs. 12889.88
Q8. You need to have Rs56, 000.00 in 8 years. If you place Rs1, 000.00 into a savings account today, what interest rate per year must you earn in order to have the required amount?
Answer – 8
Given,
Future value = Rs. 56,000
Present value = Rs. 1,000
Time Period = 8 years
We need to find the rate of interest at which we must earn in order to have the required amount.
Solution:-
FV =PV (1+i)^n
56000 = 1000(1+i)^8
=0.65 i.e. 0.65*100 = 65%
Therefore, the rate of interest is 65%
Q9. You need to have Rs57, 000.00. If Rs18, 000.00 is placed into a savings account today that pays annual compound interest of 16%, how many years will it be before you have the required amount?
Answer – 9
Given,
Future value = Rs. 57,000
Present value = Rs. 18,000
Rate of interest = 16%
We need to find the time period by which we will get the return.
Solution:-
Future value=present value (1+rate/100)n
57,000=18,000(1+16/100)n
Log 57 = Log18+ n log 1.16
n = 8.33
Therefore, the time period is 8.33.
Q10. Bank A is advertising that they are paying compound interest of 9%, compounded Semi-annually. What rate would Bank B advertise if they compound Quarterly? (Convert Bank A's rate to Bank B's compounding interval)
Answer – 10
Solution:-
For solving the above question we assume the amount to be as Rs. 1000 then when the rate is calculated semi annually then time period=6*2=12
When compounded quarterly will give = 6*4=24 (since the rate of bank A is being converted into rate of bank B)
When compounded semi annually:
We write the expression as 1000(1+9/100) ^12 which comes out to be Rs 2812 (equation 1)
When compounded quarterly:
We write the expression as 2812(1+r/100) ^24 (equation 2)
When the equation 1 & 2 is solved we get the rate as 39%.
Analysis
Answer – 1
For the new monthly payments be after you refinance the borrowed amount is to be calculated using the present value of annuity in order to get our desired output.
Answer – 2
Ramesh and Laxmi has to pay some extra amount if they wants to payoff in 15 years which is to be calculated using Net Factor of Annuity.
Answer – 3
We find out that when we retire after 24 years we are left with a desired amount using the formula of future value of the savings and stock.
Answer – 4
For calculating the amount left at the end of 16 mts we calculate it through annuity.
Answer – 5
The amount of money that will have accrued if he leaves the money in the bank for 19 years by calculating it through Future Value.
Answer – 6
Money that must be deposited today in order to have the required amount is to be calculated using Future Value.
Answer – 7
The APY(Annual Percent Yeild) on this investment is to be calculated using its formula.
Answer – 8
Interest rate per year must you earn in order to have the required amount through Future Value.
Answer – 9
Years that will be needed before you have the required amount is to be calculated by Future Value.
Answer – 10
Rate at which would be taken by Bank B advertise if they compound Quarterly will be calculated by Compound rate of interest.
