Liberal Arts Mathematics
Answer the following problems from Section 6.4 of the textbook: 11 - 14, 19 - 22, 35, 37.
For reference, the text of the problems are duplicated below.
In the following exercises, rewrite the percent in decimal form.
11. Principal = $13,800, annual interest rate = 2.55%, compounded quarterly, for 18 years
12. Principal = $150,000, annual interest rate = 2.95%, compounded quarterly, for 30 years
13. Principal = $3,500, annual interest rate = 2.9%, compounded monthly, for 7 years
14. Principal = $1,500, annual interest rate = 3.23%, compounded monthly, for 30 years.
19. Future value = $1,500,000, annual interest rate = 4.81%, compounded quarterly, for 35 years
20. Future value = $750,000, annual interest rate = 3.95%, compounded quarterly, for 10 years
21. Future value = $600,000, annual interest rate = 3.79%, compounded monthly, for 17 years
22. Future value = $800,000, annual interest rate = 4.23%, compounded monthly, for 35 years
35. Daria invests $2,500 in a CD that yields 3.5% compounded quarterly for 5 years. How much is the CD worth after those 5 years?
37. Georgita is shopping for an account to invest her money in. She wants the account to grow to $400,000 in 30 years. She finds an account that earns 4.75% compounded monthly. How much does she need to deposit to reach her goal?
11. $21,806.58
12. $362,269.29
13. $4,286.70
14. $3,947.82
19. $281,395.75
20. $506,239.96
21. $315,337.97
22. $182,493.58
35. $2,975.85
37. $96,474.38
#11 should be $21,806.58 ( FV = 13800 * ( 1 + 0.0255/4 ) \^ 18*4 = 13800*(1.006375)\^72 = 13800*1.58019 = 21806.57911…, round to 21806.58 )
#12 should be $362,269.29 ( FV = 150000 * ( 1 + 0.0295/4 ) \^ 30*4 = 150000*(1.007375)\^120 = 150000*2.41513 = 362269.284…, round to 362269.29 )
#13 should be $4,286.70 ( FV = 3500 * ( 1 + 0.029/12 ) \^ 7*12 = 3500*(1.002417)\^84 = 3500*1.22477 = 4286.703709…, round to 4286.70 )
#14 should be $3,947.82 ( FV = 1500 * ( 1 + 0.0323 / 12 ) \^ 30*12 = 1500*(1.00269)\^360 = 1500*2.63188 = 3947.819223…, round to 3947.82 )
#19 should be $281,395.75 ( PV = 1500000 / ( 1 + 0.0481 / 4 ) \^ 35*4 = 1500000/(1.012025)\^140 = 1500000/5.33057 = 281395.7413…, round up to 281395.75 )
#20 should be $506,239.96 ( PV = 750000 / ( 1 + 0.0395 / 4 ) \^ 10*4 = 750000/(1.009875)\^40 = 750000/1.48151 = 506239.9538…, round up to 506239.96 )
#21 should be $315,337.97 ( PV = 600000 / ( 1 + 0.0379 / 12 ) \^ 17*12 = 600000/(1.00316)\^204 = 600000/1.90272 = 315337.9671…, round up to 315337.97 )
#22 should be $182,493.58 ( PV = 800000 / ( 1 + 0.0423 / 12 ) \^ 35*12 = 800000/(1.003525)\^420 = 800000/4.38372 = 182493.5798…, round up to 182493.58 )
#35 should be $2,975.85 ( FV = 2500 * ( 1 + 0.035 / 4) \^ 5*4 = 2500*(1.00875)\^20 = 2500*1.19034 = 2975.849498…, round to 2975.85 )
#37 should be $96,474.38 ( PV = 400000 / ( 1 + 0.0475 / 12 ) \^ 30*12 = 400000/(1.00396)\^360 = 400000/4.14618 = 96474.37598…, round up to 96474.38).