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**Unformatted text preview: **he number of compounding per year ◦ n is the number of years Dynamo Ltd is expecting annual payments of $34225 for the next 7 years from a customer. What is the present value of this annuity if the discount rate is 8.5 per cent? Solution: m=1 Dynamo Ltd is expecting annual payments of $34225 for the next 7 years from a customer. What is the present value of this annuity if the discount rate is 8.5 per cent? Solution (Same Math: without using Formula) PV of the 1st cash flow =
PV of the 2nd cash flow = Total PV = $175181.13 PV of the 3rd cash flow =
PV of the 4th cash flow =
PV of the 5th cash flow =
PV of the 6th cash flow =
PV of the 7th cash flow = Same result using Formula – Yet, formula
Is better particularly
since (m X n) can be
large Extra Math Involving Ordinary Annuity
You have borrowed $10,000, repayable by equal halfyearly instalments for five years. If interest is 5% p.a. compoundedhalfyearly, what will be your halfyearly repayments? Solution:
1 1− (1 + i / m)m x n PVAn = (CF / m) × i/m PVAn = $10,000; CF = ?; m = 2; i = 5% = 0.05; n = 5
1 1− (1 + 0.05 / 2)2 x 5 10,000 = (CF / 2) × 0.05 / 2 10,000 = CF x 4.376032
CF=$2285.18 This CF=$2285.18 is annual. So, halfyearly repayment is CF/2 = $2285.18/2 = $1142.59 Annuity
Future Value of Ordinary Annuity (1 + i / m)m x n − 1 FVAn = (CF / m) × (i / m) ◦ CF is the series of e...

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