HW3 sol

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Finance

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Apr 3, 2024

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Homework 3 Section G (2 credit) Siddh Saraogi 02/10/22 1. Compare the interest earned by $1,000 for five years at 8% simple interest with that earned by the same amount for five years at 8% compounded annually. P = $1000 i = 8% t = 5 simple interest F = P(1 + it) = 1000(1 + (8% * 5)) = 1000(1+0.40) = $1400 Interest earned = F – P = 1400 – 1000 = $400 Compound interest F = P(1+i)^t = 1000(1+ 0.08)^5 = $1469.33 Interest earned = F – P = 1469.33 – 1000 = $469.33 Interest earned by compounding is greater than interest earned simply. 2. You are about to borrow $10,000 from a bank at an interest rate of 9% compounded annually. You are required to make five equal annual repayments in the amount of $2,571 per year, with the first repayment occurring at the end of year 1. Show the interest payment and principal payment in each year. Year Principal (P, $) Interest at 9% ($) Payment made($) Balance due ($) 1 10,000 900 2,571 8,329 2 8,329 749.61 2,571 6,507.61 3 6,507.61 585.68 2,571 4522.29 4 4522.29 407.00 2571 2358.30 5 2358.30 212.25 2571 -0.45 3. Suppose you have the alternative of receiving either $12,000 at the end of five years or P
dollars today. Currently you have no need for money, so you would deposit the P dollars in a bank that pays 5% interest. What value of P would make you indifferent in your choice between P dollars today and the promise of $12,000 at the end of five years? F = $12,000 I = 5% T = 5 years (P/F, I, t) = 1/(1+i)^t P = F(P/F, I, t) = F/(1+i)^t = 12,000/(1+0.05)^5 = $9,402.31 At an interest rate of 5% for 5 years, $9,402 would equal $12,000 and is the value for P to make the choice indifferent 4. You bought 5,000 shares of Company A's stock at $28 a share. Your intention is to hold the stock until your investment doubles in value. If you project 12% annual growth for the value of Company A's stock, how many years do you expect to hold it to reach your goal? How long for it to triple in value? P = 5,000*28 = $140,000 F = 2*P = $280,000 I = 12% F = P(1 + i)^t (1+i)^t = F/P Taking natural log t*ln(1+i) = ln(F/P) t= ln(F/P) / ln(1+i) t= ln(2) / ln(1+ 0.12) t= 6.11 years for F = 3*P
t = ln(3) / ln(1+0.12) t = 9.69 years so it will take 6.11 years to double the investment and 9.69 years to triple the investment. 5. What annual deposit is required for 5 years to accumulate an amount of money with the same purchasing power as $680.58 today, if the market interest rate is 10% per year and inflation is 8% per year? P1 = $680.58 i1 = 8% i2 = 10% t = 5 years F = P1(1+i1)^t F = 680.58(1+0.08)^5 = $1000.00 A2 = F * i/((1+i)^t – 1) A2 = 1000*0.10/((1.10)^5 – 1) = $163.80 An annual deposit of $163.80 is required for 5 years to accumulate an amount of money with the same purchasing power as $680.58 today. 6. Four annual deposits of $2,000, $1,600, $1,200, and $800 are made into a fund that pays in- terest at a rate of 11% compounded annually. Determine the amount in the fund immediately following the 4th deposit. Year Principal Deposit Interest at 11% Balance 1 0 2000 220 2220 2 2220 1600 420.20 4240.20 3 4240.20 1200 598.42 6038.62 4 6038.62 800 There is $6838.62 in the fund immediately following the 4 th deposit
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