Question

Sixty years ago, your grandparents opened two savings accounts and deposited $200 in each account. The first account was with City Bank at 3 percent, compounded annually. The second account was with Country Bank at 3.5 percent, compounded annually. Which one of the following statements is true concerning these accounts?The Country Bank account is currently worth $1,526.08.The City Bank account has earned $211.19 more in interest than the Country Bank account.The Country Bank account has paid $367.48 more in interest than the City Bank account.The Country Bank account has paid $397.30 more in interest than the City Bank account.The City Bank account is currently worth $1,201.54.

Answer 1

the true statement is The Country Bank account has paid $397.30 more in interest than the City Bank account

Step-by-step explanation:

Given:

Time, n = 60 year

Principle amount = $200

Rate of interest in City bank = 3%

Rate of interest at country bank = 3.5%

Now,

present value = Principle × ( 1 + rate )ⁿ

therefore,

The present value in city bank

Present value = $200 × ( 1 + 0.03 )⁶⁰

or

Present value = $1,178.32

and,

The Present value in country bank

Present value = $200 × ( 1 + 0.035 )⁶⁰

or

Present value = $1,575.61

Difference in interest = $1,575.61 - $1,178.32 = $397.29 ≈ $397.30

Hence,

the true statement is The Country Bank account has paid $397.30 more in interest than the City Bank account