Question

(Related to The Business of Life: Saving for Your First House) (Future value) You are hoping to buy a house in the future and recently received an inheritance of $16,000. You intend to use your inheritance as a down payment on your house. a. If you put your inheritance in an account that earns 8 percent interest compounded annually, how many years will it be before your inheritance grows to $34,000? b. If you let your money grow for 9.75 years at 8 percent, how much will you have? C. How long will it take your money to grow to $34,000 if you move it into an account that pays 4 percent compounded annually? How long will it take your money to grow to $34,000 if you move it into an account that pays 11 percent? d. What does all this tell you about the relationship among interest rates, time and future sums? a. If you put your inheritance in an account that earns 8 percent interest compounded annually, how many years will it be before your inheritance grows to $34,000? 9.79 years (Round to one decimal place.) b. If you let your money grow for 9.75 years at 8 percent, how much will you have? (Round to the nearest cent.)

Answer 1

The answers are as follows:

Please note that your solution to Question (a) is correct re. 9. 79 years (Piv) i = period. Solution to Question (a): Future Value (F.v)- Present Vahee x (1+i)" where Interest per no Number of periods ::$ 34000 = $16000x ( 178°/)? (1+86). )^. 34000 16000 or, (1+806.)? 2.125 By Trial and Error Method, Let na 1.999 7 2.125 Letns 10 , C1+8/10.2.159 2./25 1.999 10 2.159 2-105 - 1.999 10-9 2.159-1.999 x- 0.126 0.16 (1+87)? ) 1 . a 2.125 ar X 9 or V

or, = 0.787579 9.7875 . na 9.79 years (rounded off) solution to Question (b): f. V = $16000 X (1+897.) 9.75 16000 x 2:117783771 $ 33884.54034 $ 33884.54 (rounded oft) 20 Solution to Question (c): $34000 $ 16000X (1+40%.)? or, (1 + 4/.). 2.125 By Trial and Error Method, Let na 19,(1740/71921107 2.125 Let na 20, (1746) 2:1917 2.125 19 2.107 20 -→ 2:19] - 2.125-2.107 20-19 2.191-2.101 0.018 0.084 .. X 2.125 ori H-19 or 2-19

or X- 0.22 +19 X = 19.22 no 19.22 years . move Now, you into an your money account that pays 11 percent then, $34000 = $16000X (1+14.8.)" Or, (1 +11%) 2.125 By Trial and Error Method, Lel ns7 (+117.) 2.076 € 2.125 Let n=8, (1+11%)8= 2.305+2:125 2.076 2.305 x- 2.125- 2:076 8-7 2.305-2.076 8 X2 7 8 -2.125 On 07 x- 0.049 0.229 1 or x = ) ... 0:2277 7:22 years 0 no 7. 22 years

as well as on a Solution to Question (d): Power of Compounding : Compounding is the is the process whereby interest is credited to an existing principal interest already paid. The lesson to take from calculating compounding lumpsum is that Higher the interest rate lesser will be the time taken to reach the future goal, keeping the future sum constant. When i = 4%, n=19. 22 yeare =11%, 7.22 years, as per calculation in Question (c). Now, as per Calculation in Question(a)and (6) When, ė= 8%. 9.-49 yecas, FV-$34000 i=8%, 9.75 years, fv-833884-54 So, the lesson to take from calculating compounding on a lumpsum is also that inverting for the long haul can be extremely powerful (je 1$34000) $33884-54), keeping interest rate constant. Da n = ) n. be