Question

Rosa invests $3500 in an account with an APR of 5% and annual compounding. Julian invests $3000 in an account with an APR of 6% and annual compounding. complete parts a through c

a. after 5 years Rosa will have a balance of approximately: after 20 years Rosa will have a balance of approximately:

after 5 years Julian will have a balance of approximately: after 20 years Julian will have a balance of approximately:

b. Determine for each account and for 5 and 20 years, the percentage of balance that is interest.

after 5 years approximately % of Rosas balance is interest. After 20 years approximately % of Rosas balance is interest.

after 5 years approximately % of Julians balance is interest. After 20 years approximately % of Julians balance is interest.

c. Comment on the effect of interest rates and patience

choose the correct answer below

a. the percent of balance that is interest is the same after 5 years and 20 years

b. A lower initial principal with a higher APR will always have a lower balance than a higher initial principal with a lower APR.

c.A lower initial principal with a higher APR over a long enough time period can result in a higher balance than a higher initial principal with a lower APR.

b.

Answer 1

A: Future value = Present value*(1+rate)^n

After 5 years Rosa will have a balance of 3500*(1+5%)^5 = 4466.99

After 20 years Rosa will have a balance of 3500*(1+5%)^20 = 9286.54

After 5 years Julian will have a balance of 3000*(1+6%)^5 = 4014.68

After 20 years Julian will have a balance of 3000*(1+6%)^20 =9621.41

B: % that is interest = (FV-PV)/PV

Rosa:

After 5 years % that is interest = (4466.9855-3500)/3500 = 27.63%

After 20 years % that is interest = (9286.54-3500)/3500 = 165.33%

Julian :

After 5 years % that is interest = (4014.6767-3000)/3000 = 33.82%

After 20 years % that is interest = (9621.41-3000)/3000 =220.71%

C: The total value of the investment will increase even if the rate of interest is lower but over a greater period of time. However due to the effect of compounding even a lower principal will accumulate to a high value. Longer the period of investment higher will be the Future value.

a is false as the percentages are different.

B is False. The lower principal will become more than the higher principal over a longer period of time.

C is true because a lower capital will become greater than a higher principal if invested over a longer period if the APR is higher.