Question

BE6.7 (LO 2) John Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of $400,000. He estimates that the boat he wants will cost $300,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 8% (compounded annually) to buy the boat at retirement? BE6.8 (LO 2) Refer to the data in BE6.7, Assuming quarterly compounding of amounts invested at 89%, how much of John Fillmore's inheritance must be invested to have enough at retirement to buy the boat? BE6.9 (LO 3) Morgan Freeman is investing $9,069 at the end of each year in a fund that earns 5% interest. In how many years will the fund be at $100,000? BE6.11 (LO 4) Leon Tyler's VISA balance is $793.15. He may pay it off in 12 equal end of month payments of $75 each. What interest rate is Leon paying? BE6.12 (LO 4) Maria Alvarez is investing $300,000 in a fund that earns 4% interest compounded annually. What equal amounts can Maria withdraw at the end of each of the next 20 years? BE6.13 (LO 3) Adams Inc. will deposit $30,000 in a 6% fund at the end of each year for 8 years beginning December 31, 2020. What amount will be in the fund immediately after the last deposit?

please show me how to solve using a financial calculator if possible....thanks in advance

Answer 1

6.7 We would have to use compounding formula to derive the amount to be invested today which will become $ 300,000 at the end of 5 Years. The formula for the same is as follows:-

Amount = Principal [(1+i)ⁿ]

Where "Amount" is the amount required after 5 years i.e. $ 300,000

"i" is the interest rate and "n" = No of compounding periods

Now putting these values in the formula, we get the solution:-

Principal = Amount/[(1+i)ⁿ]

= 300,000 / (1.08)⁵

= $ 204,174.96

Hence the John has to invest $ 204,174.96 of his total inherited amount to accumulate $ 300,000 at the end of 5 years

6.8 Now in this question the compounding is done quarterly, hence the interest rate "i" will be 2% (8/4) and number of periods "n" is 20 (5*4)

Now the amount to be invested is as follows:-

Principal = 300,000 / (1.02)²⁰

= $ 201,891.40

Hence the John has to invest $ 201,891.40 to accumulate $ 300,000 at the end of 5 Years

6.9 The formula for calculating the Future value of an annuity is as below:-

Future Value = Annuity Amount * [(1+i)ⁿ-1] / i

100,000 = 9069 * [(1.05)ⁿ-1] / 0.05

(1.05)ⁿ - 1 = (100,000 * 0.05) / 9069

(1.05)ⁿ = 0.5513 + 1

n = 9 Years

Hence, Morgan's funds will reach to $ 100,000 in 9 years time

6.11 Future value = Annuity Amount * [(1+i)ⁿ-1] / i

793.15 = 75 * [(1+i)¹²-1] / i

[(1+i)¹² - 1] / i = 10.575

  (1+i)¹² = (10.575 * i) + 1

(1+i)¹² = (1 + 10.575 i)

i = 12% p.a / 1% p.m

Hence Leon is paying interest @ 12% P.a. compounded monthly