Question

1-Bomac steel sets aside $5000 at the beginning of every six months in a fund to renlace equipment. If interest is 6 % con quarterly, how much will be in the 1 five years?

2- An annuity with a cash value of $14 500 earns 7% semi-annually. End-of-period, semi-annual payments to the beneficiary are deferred for 7 years, and then continue for 10 years. How much is the amount of each payment?

Answer 1

Solution to Question no. 1:

In the books of Bomac Steel

(Amount in $)

	Year - 1	Year - 2	Year - 3	Year - 4	Year - 5	Total
1st Half	2nd Half	1st Half	2nd Half	1st Half	2nd Half	1st Half	2nd Half	1st Half	2nd Half
Fund Invested	5000	5000	15000	5000	25000	5000	35000	5000	45000	5000	50000
Period of Holding	12	6	12	6	12	6	12	6	12	6
Effective Rate of Interest a (in %)	26.25	12.36	26.25	12.36	26.25	12.36	26.25	12.36	26.25	12.36
Interest Amount	1312.5	618	3937.5	618	6562.5	618	9187.5	618	11812.5	618	35902.5
Balance to be received at the end of 1st Five years	85902.5
Note: a Formula used to calculate the effective rate of interest (applying compounding principle): Interest = {1 + (r/100)}^n Where, r = Rate of interest, n = Time period; Applying 6% rate of interest compounded over 12 months (n = 4) and 6 months (n = 2), we get the Effective Rate of Interest at 26.25% and 12.36% (rounded off to two decimal places)

Solution to Question no. 2:

(Amount in $)

	Principle	Interest a	Sum Total
First Seven Years	14500	22910	37410
Second Ten Years	37410	107366.7	144776.7
Amount of each payment from the end of eighth-year b	14477.67 c
Note: a Formula used to calculate the effective rate of interest (applying compounding principle): Interest = {1 + (r/100)}^(n × t) Where, r = Rate of interest, n = Compounding Schedule and t = Time period; Applying a 7% rate of interest compounded semi-annually (n = 2) and t = 7 (for the first seven years) and t = 10 (for the second ten years) we arrived at the results displayed above.
b Since the payments to the beneficiary have been deferred for 7 years he is to receive the annuity payments from the end of the eighth year.
c Value of each payment: (144776.7 / 10) = 14477.67