1 IF 100 IS DEPOSITED AT THE END OF EACH MONTH IN A SAVINGS

1- IF $100 IS DEPOSITED AT THE END OF EACH MONTH IN A SAVINGS ACCOUNT THAT PAYS 1% INTEREST PER MONTH STARTING ONE MONTH FROM NOW, HOW MUCH MONEY WILL BE IN THE ACCOUNT AT THE END OF SEVEN YEARS?

2- TO RAISE MONEY FOR A NEW HOME, YOUR DAUGHTER ASKS YOU TO LEND HER “SOME” MONEY. SHE OFFERS TO PAY YOU $50,000 AT THE END OF FOUR YEARS. HOW MUCH SHOULD YOU LOAN HER NOW IF YOU WANT TO RECEIVE 5% INTEREST PER YEAR? NOTE: THE ANSWER IS NOT $ 0.

3- A FUND ESTABLISHED TO PRODUCE A DESIRED AMOUNT OF MONEY AT THE END OF A GIVEN TIME PERIOD, BY MEANS OF SERIES OF PAYMENTS THROUGHOUT THE PERIOD IS CALLED A SINKING FUND.   A SINKING FUND IS TO BE ESTABLISHED TO ACCUMULATE MONEY TO REPLACE A $12,000 MACHINE. IF THE MACHINE IS TO BE REPLACED AT THE END OF 10 YEARS, HOW MUCH MONEY SHOULD BE DEPOSITED IN THE SINKING FUND EACH YEAR,STARTING IN YEAR 1? USE AN INTEREST RATE OF 8%.

Solution

1. Below formula is used to calculate money in the account at the end of 7 years:

A=P*(1+r/100)^n

where A= Amount at the end

P = Principal Amount

N= Number of years

R= Rate of Interest

100*(101/100)^7 =107.21

2.Same Formula is used but here we have to calculate the Principal Value therefore:

50000=p*(105/100)^4

50000=p*(1.05)^4

P= 50000/(1.05)^4

P= 41135.12

3.Below formula is used to calculate the amount of periodic contributions:

Periodic Contribution to Sinking Fund =Par Value of Bonds to be Paid off/(1 + r_s)ⁿ 1/r_s

where : r_s is the rate of return earned by the money deposited in the sinking fund

=12000/((1.08)^10-1)/0.08

=129430.3

=129430.3/10 = 12943.03 This amount has to be deposited in sinking fund starting from year 1.