Question

What is the discounted value of

$844

paid at the end of every

three months

for

10

years if interest is

9 %

per annum compounded monthly..

Please provide the appropriate formula and show work. Please do not use excel.

Answer #1

**$ 22,043.19**

Step-1:Calculation of equivalent 3 month's interest rate | |||||||

(1+i)^n | = | (1+i)^n | Where, | ||||

(1+0.0075)^3 | = | (1+i)^1 | Monthly interest rate | = | 9%/12 | ||

1.022669 | = | 1+i | = | 0.0075 | |||

0.022669 | = | i | |||||

thus, | |||||||

Equivalent 3-months interest rate | = | 0.02266917 | |||||

Step-2:Calculation of discounted value | |||||||

Discounted Value | = | Cash Flow every 3 months | * | Present Value of annuity of 1 | |||

= | $ 844.00 | * | 26.11753 | ||||

= | $ 22,043.19 | ||||||

Working: | |||||||

Present Value of annuity of 1 | = | (1-(1+i)^-n)/i | Where, | ||||

= | 26.1175264 | i | = | 0.022669 | |||

n | = | 40 | |||||

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