Question
Kiran invested $1,500 in an account paying an interest rate of 8\tfrac{1}{4}8 4 1 % compounded continuously. Isaac invested $1,500 in an account paying an interest rate of 7\tfrac{5}{8}7 8 5 % compounded daily. After 6 years, how much more money would Kiran have in his account than Isaac, to the nearest dollar?
Answer
$197
- Find the value of Kiran's investment after 6 years V_K using the continuous compounding formula: V_K = P*e^(r*t), where P is the principal amount, r is the annual interest rate as a decimal, and t is the number of years. A: V_K = 1500*e^(0.0825*6) = $2,291.63
- Find the value of Isaac's investment after 6 years V_I using the daily compounding formula: V_I = P*(1+r/n)^(n*t), where n is the number of times interest is compounded per year, which is 365 for daily compounding. A: V_I = 1500*(1+0.078125/365)^(365*6) = $2,094.20
- Calculate the difference in value between Kiran and Isaac's investments. A: $2,291.63 - $2,094.20 = $197.43 rounded to the nearest dollar is $197.