Question

A businessman borrowed P3,000,000 with interest at the rate of 6% compounded annually. He agrees to discharge his obligations by paying a series of 6 annual payment, the first being due at the end of the fifth year. Determine the value of his annual payment. A. 500,000 B. 770,222 C. 726,625 D. 600,000

Answer 1

Answer:

B. 770,222

Step-by-step explanation:

From the question above, we are given the following values:

Principal = 3,000,000

Interest rate = 6%

Step 1

Since we are told in the question that he will make 6 payments at the end of each year STARTING FROM THE END OF THE FIRTH YEAR, the first step would be to find the future value of the Principal (3,000,000) for the first 4 years.

Future Value formula =

FV = P × {(1 + r)ⁿ

Where P = Principal = 3,000,000

r = interest rate = 6% = 0.06

n = number of years = 4 years

Future value = 3,000,000 × {( 1 + 0.06)⁴

Future value = 3,787,430.88

Hence, the future value of this loan at the end of year 4 is 3,787,430.88.

Step 2

We are told in the question that he would be carrying out a series of series of 6 annual payment, the first being due at the end of the fifth year.

Therefore, this means the future value at the end of four year would be equal to or equivalent to the present value at the beginning of the fifth year.

The second step to take would be to find the periodic payment.

The forward for periodic payment is given as:

Periodic Payment ( Pmt) = (PV × r) ÷ ( 1 - (1 + r) ⁻ⁿ  

Present value( PV) = 3,787,430.88.

number of time periods = 6

interest rate per time period(r) = 6%

payments are made at the end of each time period.

Periodic Payment ( Pmt) = (3,787,430.88. × 0.06) ÷ [( 1 - (1 + 0.06)⁻⁶)]

= 770,221.9

Approximately = 770,222

Therefore, the value of his annual payment with his first payment been due at the beginning of the fifth year is 770,222.