Problem 6-16 Calculating Future Values [LO1] What is the future value of $1,800
ID: 2641066 • Letter: P
Question
Problem 6-16 Calculating Future Values [LO1]
What is the future value of $1,800 in 19 years assuming an interest rate of 7.1 percent compounded semiannually? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
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Problem 6-19 EAR versus APR [LO4]
Big Dom
What is the future value of $1,800 in 19 years assuming an interest rate of 7.1 percent compounded semiannually? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
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Problem 6-19 EAR versus APR [LO4]
Big Dom
Explanation / Answer
Answer to part 1.
Future value = CAsh flow at period 0 * (1 + r)n = 1800 * (1 + 0.0355)38 = $6,776.05
where, r = rate of interest = 7.71 / 2 = 3.55 (since compounded semi annually),
n = time period = 19*2=38
Answer to part 2
Annual Percentage Rate (APR) is the equivalent interest rate considering all the added costs to a given loan. Naturally, it is a function of the loan amount, the interest rate, the total added cost, and the terms. The APR would equal the interest rate if there is no additional costs to a given loan.
Since, other components are not available, so APR will be equal to the interest rate.
Therefore, APR = 26.2%
Effective Annual Rate Formula
i = (1 + r/m)^m - 1
Where r = R/100 and i = I/100; r and i are interest rates in decimal form. m is the number of compounding periods per year. The effective annual rate is the actual interest rate for a year.
Therefore, i = (1 + 0.262 / 12) ^ 12 - 1 = 29.59% (EAR)
Answer to part 3.
Live Forever LIfe Insurance Co.
Return = MOnthly payout / Present value *100 = 1450 / 114000 * 100 = 1.27%
APR = 1.27% * 12 = 15.24%
EAR = (1 + 0.1524 / 12) ^ 12 -1 = 16.35%
Answer to part 4.
PV of cash flows
DCF = CF1/(1+r)1 + CF2/(1+r)2 + CF3/(1+r)3 ...+ CFn/(1+r)n
where, r = 9 / 4 = 2.25% (compounded quarterly)
DCF or PV = 810 / (1 + 0.0225)4 + 890 / (1 + 0.225)8 + 0 / (1 + 0.225)12 + 1480 / (1 + 0.225)16 = $2,522.59 ?