Question

Gregory may choose between two accounts in which to invest $5000. account a offers 2.3% annual interest compounded monthly. account b offers continuous compound interest. greg plans to leave his investment untouched (no further deposits and no withdrawals) for 10 years

which account will yield the greater balance at the end of 10 years?

Answer 1

Account B, which offers continuous compound interest, will yield a greater balance at the end of 10 years than Account A, which offers 2.3% annual interest compounded monthly.

Step-by-step explanation:

To determine which account will yield a greater balance at the end of 10 years, we need to compare the compounded interest for each account. For Account A with a 2.3% annual interest compounded monthly, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we get A = 5000(1 + 0.023/12)^(12*10) = $5910.86.

For Account B with continuous compound interest, we can use the formula A = Pe^(rt), where A is the final amount, P is the principal amount, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the number of years. Plugging in the values, we get A = 5000e^(0.023*10) = $5930.84. Therefore, Account B will yield a greater balance at the end of 10 years.