Quiz 3 A P&ACO has an investor loan of S300,000 in 6 years. How much must be dep
ID: 1141183 • Letter: Q
Question
Quiz 3 A P&ACO has an investor loan of S300,000 in 6 years. How much must be deposited today into 6% fund to obtained the required amount? 1- F- 6,ov01,461 F-38,814 2. A Van Gogh painting of Sunilowers was sold in 1987 at auction for $40,000,000. The original selling price in 1889 was the equivalent of $100. What is the return on investment (ROI) of this painting? 3. If SS,000 is invested today into a 5% accoun years required using logarithms t and it accumulates to $9,000, determine the number of If $6,000 is obtained from a loan at 8% interest, to be repaid with a single payment in 5 years, what is the total amount to be repaid? 4.Explanation / Answer
Answer in response to Question 2
The Return on Investment (RoI) of an investment is computed as the ratio (or percentage) of the gain made from an investment to the cost of the investment.
The investment made in purchase of Van Gogh painting of sunflowers in 1889 is $100 whereas the proceeds from the sale of this painting in 1998 is $40,000,000 The gain of this investment is computed as the difference between Sale proceeds and investment cost i.e., $40,000,000- $100 which comes out to be $39,999,900. Thereafter, RoI is computed by dividing this gain from investment by the cost of investment i.e., $$39,999,900/ $100 which comes out to be $3,99,999. Expressed in % the RoI is 3,99,999,00%.
Answer in response to Question 3
Amount = Principal (1+ Interest rate)^number of years
=> A = P *(1+r)^n ------(1)
Amount (denoted by A) is the total amount accumulated including interest compunded on investment. In this question, A=$9000
Principal (denoted by P) is the initial sum of money invested today. In this question, P=$5000
Interest rate (denoted by r) is the compound rate of .interest on principal invested today.In this question, r=5% (or 0.05)
Number of years (denoted by n) is the duration for which the principal remains invested i.e. the number of years for which the interest on principal is compounded.
Thus, substituting values of A, P, and r in (1) above we get the following :-
9000 = 5000* (1+ 0.05)^n
=> 9000 = 5000* (1.05)^n
Taking natural logarithms on both sldes, we get the following:-
=> log (9000) =log (5000) + nlog (1.05)
=> 9.10 =8.52 +n (0.05) [Values of logarithms rounded of to two decimal paces]
=> (9.10-8.52)/(0.05) =n
=> (0.58)/(0.05) =n
=> 11.88 =n
=> n = 12 years (value rounded off)
Thus, the number of years is 12 years
Answer in response to Question 4
Amount = Principal (1+ Interest rate)^number of years
=> A = P *(1+r)^n ------(1)
Amount (denoted by A) is the total amount to be repayed towards loan including the interest compunded on principal loan amount.
Prncipal (denoted by P) is the principal amount of loan taken. In this question, P=$6000
Interest rate (denoted by r) is the compound rate of .interest on principal loan amount taken.In this question, r=8% (or 0.08)
Number of years (denoted by n) is the duration for which the loan is taken post which the loan will be repaid. In this question, n=5
Thus, substituting values of P, r and and n in (1) above we get the following :-
A= 6000* (1+ 0.08)^5
=> A= 6000* (1.08)^5
=> A= 6000* (1.08)^5
=> A =6000 *( 1.4693)
=> A =8815.968
=> A =8816 (rounded off)
Thus, the total amount to be repaid as a single payment in 5 years is $8,816.
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