Question

Please, elaborate on solutions

Part B 1. Melinda has a savings account that earns interest at 6% per annum. She opened her account with $1000 on December 31. How much interest will she earn during the first year if a) the interest is compounded daily b) the interest is calculated daily and paid into the account on June 30 and December 31; c) the interest is calculated daily and paid into the account at the end of each month?

Answer 1

here , we will first calculate the effective rate of interest for each part based on the compounding frequency or the no. of times interest is paid in 1 year, if interest is paid at the end of 6 months , the compounding frequency = 2 , since there are two semi-annual or 6 month periods in one year. similarly for monthly compounding the compounding frequency will be 12

after calculating the effective rate of interest based on the formula (as can be seen in the image below) , we will calculate the interest earned during 1st year , by multiplying the effective interest rate with the amount deposited

1 interest rate 0.06 2 amount deposited 1000 compounding compounding frequency effective interest rate interest earned during 1st year daily semi-annually monthly 6.18% 6.09% 6.17% 365 61.84 60.90 61.68 12

C. 1interest rate 0.06 1000 compounding daily semi-annually monthly 2 amount deposited compounding frequency effective interest rate 365 interest earned during 1st year -D4*$B$2 -EXP(B1)-1 5 b 12