Question

1. Find the present value of a series of quarterly payments of P950 each, the first payment is due at the end of 2 years and 3 months and the last at the end of 5 years and 6 months. If the money is worth 15% compounded quarterly.

2. Find the monthly payment for 36 periods to discharge an obligation of P88000 if the money is worth 12%, m=12 and the first payment is due at the end of 1 year and 3 months.

Answer 1

Question 1:

Payments - P 950

First payment - 2 years and 3 months from today

Last payment - 5 years and 6 months from today

Discount rate - 15%

Compounded quaterly

Effectie rate - 15/4 = 3.75%

1 year = 4 quaters

2 years and 3 months - 9 periods

5 years and 6 months - 22 periods

PV of series = Sum of PV of each payment = 950 / ( 1 + rate/100)^period

using excel we get:

Thus, the present value is P 7599.9

Question 2:

Principal - P 88000

Rate = 12%

Monthly payments

Effectie rate - 1%

Periods - 36 or 3 years

To find the Monthly payment we need to first find the amount of principal in 1 year and 3 months, considering monthly compounding:

Principal - 88000* ( 1 + 1/100)^15 [ 1 year and 3 months is equal to 15 months, rate per month is 1%]

= 88000 * 1.01^15

= 88000 * 1.16097

Principal = 102,165.2681

Monthly payment = Principal * Rate per period * ( 1 + rate per period ) ^ total periods / (( 1 + rate per period ) ^ total periods -1 )

= 102,165.2681 * 0.01 * ( 1+ 0.01)^36 / ( ( 1+ 0.01)^36 - 1)

= 1021.65268 * 1.01^36 / 1.01^36 - 1

= 1021.65268 * 1.431 / 0.431

= 3392.0765

Thus monthly payments are - P 3392.0765