Homework SourseMarsha and Jan both invested money March 1 2007 Marsha inves
| Marsha and Jan both invested money March 1, 2007. Marsha invested $7,000 at Bank A where the interest was compounded quarterly. Jan invested $4,000 at Bank B where he interest was compounded continuously. On March 1, 2010, Marsha had a balance of $8,481.69 while Jan had a balance of $4,726.24. What was the interest rate at each bank? (Round to the nearest tenth of a percent) |
| Marsha and Jan both invested money March 1, 2007. Marsha invested $7,000 at Bank A where the interest was compounded quarterly. Jan invested $4,000 at Bank B where he interest was compounded continuously. On March 1, 2010, Marsha had a balance of $8,481.69 while Jan had a balance of $4,726.24. What was the interest rate at each bank? (Round to the nearest tenth of a percent) |
Solution
t = 3 yrs
Marsha investment :
compounded quartely : A = P(1 +r/400)^(3*4)
8481.69 = 7000( 1 + r/400)^12
1.21 = ( 1 + r/400)^12
take ln on both sides:
ln(1.21) = 12ln( 1+ r/400)
0.0159 = ln( 1 +r/400)
1.016 = 1 +r/400
r=0.016*400 = 6.39 = 6.4% interesr rate
Jan\'s investment:
compounded conitinously: A = Pe^(r*t)
4726.24 = 4000e^(3r)
1.181 = e^3r
take ln on both sides:
ln( 1.181) = 3r
r =0.0556
r = 5.6 % interest rate
