Question

Explain what every term means in the two formulas below and explain what they are used to calculate.

Then pick the appropriate formula to solve the problems.

| πι Σα 1 - 1 + 1 - 1

Answer 1

the first formula is present value of annuity it determines the present value of all the future payments made at a given time .

PVAF=A[(1+i)^n-1/(i(1+i)^n)

A=annuity or the annual payment to be made.

i=interest rate which can be compounded quarterly(i/4) , monthly(i/12) or yearly(i)

n=number of years .

Second formula is Future value of annuity=A[(1+i)^n-1]/i.

A=annual payment which is to be made now to accumulate to a future amount. i=interest rate , n=number of years.

For the first problem Present value of annuity has to be used for the second problem Future value of annuity has to be used.

11)The property valued is 125000 but down payment of 125000*0.25 is already made and since its quarterly compounded n is now 21.5*4=86 and interest rate is i/4 therefore 0.0086/4=0.00215.

=125000-(125000*0.25)=A[(1+0.086/4)^(21.5*4)-1]/[(0.086/4)(1+0.086/4)^^21.5*4]

=93750=A(5.2301701/0.1339487)

A=2401.0092

Hence the size of the Quarterly payments is 2401.0092

12)monthly payments hence n is now 12n and i=i/12

=50000=1000[(1+0.09/12)^12n-1]/(0.09/12)

50=[(1+0.0075)^12n-1]/(0.0075)

50=1.0075^12n-1/(0.0075)

=50*0.0075=1.0075^12n-1

0.375+1=1.0075^12n

=1.375=1.0075^12n

log(1.375)=12nlog(1.0075)

0.138=12n0.00324

12n=0.138/0.00324

12n=42.59

N=n=42.59/12

n=3.55

hence 3.55 years to find out in months it is 3 years 7 months (0.55*12=6.6 is approximately 7 months).