Question

Gough wishes to save some money for a trip to Antarctica. He plans to make regular payments of $1,000 per month for the next 3 years into an account at Mawson Mutual Bank that earns 7% interest per annum compounded half-yearly. The first payment will be made immediately. The future value of Gough’s savings one month after the last payment will be

Select one:

a. $38,269.51

b. $40,099.47

c. $39,856.49

d. $41,158.77

Answer 1

Periodic monthly Deposit at the beginning of each month = $1,000

Interest Earned on account = 7% per annum compounded half-yearly

Since, Interest is compounded semi-annually while deposits are monthly. We will calculate the Nominal Interest rate compounded monthly to be used in Future Value calculations

Calculating Effective Interest Rate:-

where, r = Periodic Interest rate = 7%

m = no of times compounding in a year = 2 (semi-annual compounding)

EAR = 7.1225%

Now, Using EAR to calculate the Nominal Interest rate compounded monthly:-

where, r = Periodic Interest rate

m = no of times compounding in a year = 12 (Monthly compounding)

Taking 12-root on Both sides,

1.00575003950 = (1+ r/12)

0.00575003950 = r/12

r = 0.0690005 or 6.90005%

So, Nominal Interest Rate monthly compounding = 6.90005%

- Calculating the Future Value of periodic deposit using Future Value of Annuity due formula:-

Where, C= Periodic Payments = $1,000

r = Periodic Interest rate = 6.90005%/12 = 0.57500416666%

n= no of periods = 3 years*12 = 36

Future Value = $40,099.47

So, The future value of Gough’s savings one month after the last payment will be $40,099.47

Hence, Option B