Question

1. Sometimes, in small towns, banks need to borrow smaller amounts from each other to cover certain denominations of bills and coins when they are running low.
   1. The DEF bank borrowed $10 500 for one day at a rate of j365 = 3.75% , but the next day they needed to borrow another $3750, but the rate increased to j365 = 4%
      . What does DEF Bank owe if they repay all of their debts the day after they borrowed $3750 and the rate j365 did not change?
   2. If DEF borrowed $23 750 and repaid $23 760 at the interest rate j365 = 7.5% , how long did it take them to repay the loan?

Answer 1

Calculation of the interest and the amount of repayment :

Interest = ($10500 × 3.75% × 2 day ÷ 365 days) + ($3750 × 3.75% × 1 day ÷ 365 days)

Interest = $2.158 + $0.385 = $2.543 (approximately)

Repayment = Principal + Interest = $10500 + $3750 + 2.543 = $14252.54

Calculation of number of days :

Interest = Amount of repayment - principal = $23760 - $23750 = $10

Interest rate = 7.5% for 365 days, therefore,

Interest for 1 day = $23750 × 7.5% × 1 day ÷ 365 days = $4.88

Therefore,

Number of days for which interest is $10 = $10 ÷ $4.88 = 2.05 days = 2 days ( approximately).