Question

1. You have $50,000 invested in an account paying 3.50%. If you just finished paying your total college expenses for the coming year and your college costs $19,000 per year, how many years will your money last? (Treat your costs like an annuity with the first payment one year from today.)
2. You have a choice between a lottery lump sum payout of $10,000,000 today or a series of twenty-five annual annuity payments $800,000 (first payment one year from today). At an interest rate of of 6.50%, which one do you choose?
3. Your company intends to finance the purchase of a new construction crane. The cost is $1,500,000. Compare the interest cost of three different types of loans for 10 years (discount loan, interest only loan, amortized loan) at the interest rate of 8%.

Answer 1

Q1)
Rate = 3.5%
Payment = 19000
Present Value = 50000
Nper = ?
	Excel formula	Result
Period (years)	=NPER(3.5%,19000,-50000,0,0)	2.81
Answer : Your money will last for 2.81 years
Q2)
Rate = 6.5%
Payment = 800,000
Nper = 25
Present Value = ?
	Excel formula	Result
Present Value	=PV(6.5%,25,-800000,0,0)	$                       97,58,301.38
Answer : It's better to receive $10,000,000 because the present value of 25 year annuity is $9,758,301.38 which is lower than the lump sup payment
Q3)
	Discount option	Only interest option	Amortized loan
Formula	=1500000-(PV(8%,10,0,-1500000,0))	=10*(1500000*8%)
Interest	$                                                  8,05,209.77	$                       12,00,000.00	$              7,35,442.33
Year	Interest payment formula in Excel	Interest
1	=IPMT(8%,1,10,-1500000,0,0)	$                         1,20,000.00
2	=IPMT(8%,2,10,-1500000,0,0)	$                         1,11,716.46
3	=IPMT(8%,3,10,-1500000,0,0)	$                         1,02,770.24
4	=IPMT(8%,4,10,-1500000,0,0)	$                             93,108.32
5	=IPMT(8%,5,10,-1500000,0,0)	$                             82,673.45
6	=IPMT(8%,6,10,-1500000,0,0)	$                             71,403.78
7	=IPMT(8%,7,10,-1500000,0,0)	$                             59,232.55
8	=IPMT(8%,8,10,-1500000,0,0)	$                             46,087.61
9	=IPMT(8%,9,10,-1500000,0,0)	$                             31,891.08
10	=IPMT(8%,10,10,-1500000,0,0)	$                             16,558.83
Total interest		$                         7,35,442.33