Question

Wilbur invests $4800 in a savings account that compounds interest monthly at an APR of 3.7%. Orville invests $5300 in a savings account that compounds interest annually at an APR of 3.4%. Who will have the higher accumulated balance after 5 years and after 20 years?

a) Wilbur will have a higher balance after 5 years and after 20 years.
b) Orville will have a higher balance after 5 years and after 20 years.
c) Both will have the same balance after 5 years, but Wilbur will have a higher balance after 20 years.
d) Both will have the same balance after 20 years, but Orville will have a higher balance after 5 years.

Answer 1

To determine who has the higher balance between Wilbur and Orville's investments, the compound interest formula is used for each account with respective compounding frequencies and interest rates for 5 and 20 years. After calculation, the results would reveal if Wilbur's monthly or Orville's annual compounding investment yields a higher accumulated balance.

Step-by-step explanation:

To compare the accumulated balances of Wilbur and Orville's investments, we use the compound interest formula, A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested in years.

For Wilbur's investment, which compounds monthly:

• Principal (P) = $4800
• Annual interest rate (r) = 0.037 (3.7% as a decimal)
• Compounds per year (n) = 12
• Time (t) = 5 and later 20 years

For Orville's investment, which compounds annually:

• Principal (P) = $5300
• Annual interest rate (r) = 0.034 (3.4% as a decimal)
• Compounds per year (n) = 1
• Time (t) = 5 and later 20 years

After calculating A for both for 5 and 20 years, compare the final amounts to determine who has the higher balance.

For 5 years:

Wilbur: A = 4800(1 + 0.037/12)(12*5)

Orville: A = 5300(1 + 0.034/1)(1*5)

For 20 years:

Wilbur: A = 4800(1 + 0.037/12)(12*20)

Orville: A = 5300(1 + 0.034/1)(1*20)

By plugging in values and calculating, it would be determined which option, a) through d), correctly represents whether Wilbur or Orville has the higher accumulated balance after 5 and 20 years.