Question

3.     Future and Present Value Calculations

A.        Mark J. is due to receive a cash stipend of $80,000 from a family trust at the end of five years. A relative has offered to purchase Mark’s interest in the trust fund. If Mark’s investment rate is 10%, what is the minimum amount that he should accept today for the $80,000 interest?

B.        Maria H. has decided to deposit $3,000 per year in a savings certificate account for the next 20 years. If the account is able to earn 6% per year during that time, how much will accumulate in the account at the end of the 20 years?

C.        Lucy G. has the opportunity to buy a property from which she can earn $15,000 per year in rental income for a period of 10 years. If Lucy’s investment rate is 12% per year, what is the maximum amount that she would be willing to pay today and still meet her investment criterion?

D.        Andrew M. has $20,000 to invest. How much money will Andrew have at the end of 30 years if the $20,000 lump sum is put into a retirement account and allowed to earn 8% per year for a period of 30 years?

Answer 1

A) VALUE OF $1 AT THE END OF YEAR 5 = (1/1.10)^5 = 0.621

AMOUNT TO BE ACCEPTED = 80000*0.621 = 49670 APPROX

B)

FUTURE VALUE OF ANNUITY = R[(1+i)^n-1]/i

R = CASH FLOW PER PERIOD

I = INTEREST RATE

N = NUMBER OF PAYMENTS

3000[(1+0.06)^20-1]/0.06

3000*2.207/0.06 = 110355 APPROX

C)

YEAR	BASE (12%)	PV FACTOR (A)	CASH INFLOWS [B)	PV OF CASH FLOW B*A
1	1/1.12	0.893	15000.00	13393
2	(1/1.12)^2	0.797	15000.00	11958
3	(1/1.12)^3	0.712	15000.00	10677
4	(1/1.12)^4	0.636	15000.00	9533
5	(1/1.12)^5	0.567	15000.00	8511
6	(1/1.12)^6	0.507	15000.00	7599
7	(1/1.12)^7	0.452	15000.00	6785
8	(1/1.12)^8	0.404	15000.00	6058
9	(1/1.12)^9	0.361	15000.00	5409
10	(1/1.12)^10	0.322	15000.00	4830
	NET PRESENT VALUE		84753

MAXIMUM AMOUNT SHE WOULD BE WILLING TO PAY = 84753

D)

A = P(1 + r/n) ^ nt.

A= FINAL AMOUNT

P = INITIAL AMOUNT

R = INTEREST RATE

N = NO. OF TIMES INTEREST PAID IN 1 YEAR

T= TOTAL YEARS

A = 20000(1+0.08/1)^30

=20000*10.06 = 201250 APPROX