THANK YOU IN ADVANCE!!

Question

If you invest $2100 in a money market account at an annual interest rate of 6.7%: a. How much money will you have in the account at the end of 5 years if it is compounded quarterly? __________________

b. How long (to the nearest year) will it take to grow from $2100 to $12,000 if the investment is compounded annually? __________________

c. How much would you have to invest in this account to have $20,000 in 18 years if it is compounded continuously? __________________

d. What would the rate have to be (to the nearest tenth of a percent) to have the $2100 grow to $12,000 in 10 years when compounded continuously?

Answer 1

2100 ( 1 + 0.067/4)^20 = 2927.54

-------------------------------------------------------

2100 ( 1.067)^n = 12000

1.067^n = 12000/2100 = 120/21 = 40/7

n Log (1.067) = log(40/7)

n = [log 40 - log 7]/ log 1.067

= 28.876533

-------------------------------------------------------

P exp(0.067)^18 = 20000

P = 20000/ exp(0.067)^18

P = 10234.18

------------------------------------------------

2100 exp(x)^10 = 12000

exp(x)^10 = 40/7 <--- same as #2 above

10 log(exp(x)) = log (40/7)

10 x = log (40/7)

x = 7.568619513...%