A 10-year annual annuity due with the first payment occurring at date t=7 has a current value of $50 000

A 10-year annual annuity due with the first payment occurring at date t=7 has a current value of $50 000. If the discount rate is 13% per year, what is the annuity payment amount?

Year
0 1 2 3 4 5 6 7 8 9 10

50,000 X X X X

Equation for present annual annuity due,

PVA = W x 1 - 1 x (1 + i) where PVA is the present value
(1 + i)n W is the amount required to pay
i i is the interest rate
n is the period

50,000 = W x (PVIFA13%, 4)(1 + 0.13) x 1/(1 + 0.13)6
50,000 = W x 2.9745 x 1.13 x 0.4803
50,000 = W x 1.6144
W = 30,971.70

You currently owe a finance company $6700 that you would like to pay back over the next 24 months (payments will be made at the end of the month.) The finance company is charging you 16% interest compounded quarterly. How much will your monthly payments be?

PVA = W x 1 - 1 where PVA is the present value
(1 + i)n W is the amount required to pay
i i is the interest rate
n is the period

6,700 = W x (PVIFA4%, 8)
6,700 = W x 6.7327
W = 995.14

As W is for quarterly amount, the monthly payment will be equal to

995.14/3 = 331.71