Question

A local company has K2,500 to set up an annuity to be paid quarterly for 5 years. The payments of that annuity are to be increased in line with the current interest rate. The account pays interest at 10% p.a. compounded quarterly,
a) Calculate the size of each payment during the first year.

b) What is the size of the final payment (payment at the end)?​

Answer 1

Answer:

Step-by-step explanation:

(a).

Within 1 year, there would be 4 payments to be made.

therefore, PMT= $\frac{P(1+i)}{n} = \frac{2500(1+0.025)}{4*5} =\frac{2562.5}{20} = 128.125$

(i) 1st payment will be :PMT $128.125

(ii) 2nd payment will be :128.125*(1.025)^1= $131.33

(iii) 3rd payment will be :128.125*(1.025)^2=$134.61

(iv) 4th payment will be :128.125*(1.025)^3=$137.98

Hence the payments are: $128.125, $131.33, $134.61, and $137.98.

(b).

The size of the final payment $PMT(1+i)^{m-1}$ where m 4 *5= 20

$=128.125(1+0.025)^{20-1} \\=128.125(1.025)^{19} \\= 204.83$