Question

Laura goes to a bank and opens a new account. She deposits $5,500. The bank pays 1. 6% interest compounded annually on this account. Laura makes no additional deposits or withdrawals. Which amount is the closest to the account balance at the end of 4 years? $5,852. 00 $5,860. 53 $5,940. 00 $5,954. 31.

Answer 1

The amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)

How to calculate compound interest's amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

$CI = P(1 +\dfrac{R}{100})^T - P$

The final amount becomes:

$A = CI + P\\A = P(1 +\dfrac{R}{100})^T$

For the considered case, we're given that:

• Initial amount Laura deposited = $5,500 = P
• Type of interest: Compound interest
• Unit of time: Annually
• Rate of interest = 1.6% annually = R
• Total unit of time for which amount is to be calculated: 4 years = T

The final amount at the end of 4 years in the considered account of Laura is evaluated as:

$A = 5500(1 + \dfrac{1.6}{100})^4 = 5500(1.016)^4 \approx 5860.53 \: \rm (in \: dollars)$

Thus, he amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)

Learn more about compound interest here:

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