Question

Thirty years ago, Abby invests $10,000 in an account with 3% annual interest,

compounding quarterly. Twenty years after Abby’s initial investment, Ben invests
$18,000 in an account with the same rate, also compounding quarterly. At this time, whose account has more value? (t = 30 years for Abby; and t = 10 years for Ben)

Answer 1

• Abby's account has more value

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Calculate the final amounts in each account using the formula for compound interest:

• 
  `A = P(1 + r/n)^(nt)`

Where:

• A = the future value of the investment,
• P = the investment amount,
• r = the annual interest rate (decimal),
• n = the number of compounds per year,
• t = the number of years.
  

Abby's invetsment is:

• P = $10,000, r = 3% = 0.03, n = 4, t = 30 years

Calculate the future amount:

• 
  `A = 10000(1 + 0.03/4)^(4*30)  = $24513.57`

Ben's investement is:

• P = $18,000, r = 3% = 0.03, n = 4, t = 10 years

Calculate the future amount:

• 
  `A = 18000(1 + 0.03/4)^(4*10) = $24270.28`

Comparing the account values, Abby's account has more value:

• $24513.57 > $24270.28