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Calculating Interest

Calculating Interest - An example A 5-year bond with a...

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The formula shown below will approximate the effective annual yield (interest rate) of an investment/debt where there are periodic receipts/payments of interest and a final lump-sum receipt/payment where the initial amount invested/borrowed isn’t equal to the final lump-sum receipt/payment. Y = [ I + ( P – M) / N ] / ( P + M ) / 2 Where: Y = Effective annual yield (rate) N = Number of periods of compounding in total M = Amount paid/received at date of purchase/sale P = Face/Maturity value (final lump-sum payment) I = Amount of income received/paid per compounding period A good application of this formula would be an investment/sale of a bond where the nominal (stated) interest rate is higher, or lower, than the effective (market) rate on the date of purchase/sale. Required information: (1) periodic interest receipts/payments, (2) initial investment/sales amount, and (3) final lump-sum receipt/payment (maturity value). Knowledge of the nominal (stated) interest rate is not required.
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Unformatted text preview: An example : A 5-year bond with a maturity value of $100,000.00, a stated annual interest rate of 5.000% with annual interest payments of $5,000.00 (5% x $100,000.00) is sold to yield a 6.000% effective rate. The initial amount of cash changing hands (present value) on the sales date would be $95,787.63 as determined by using present value tables. [($100,000.00 * 0.74725817) + ($5,000.00 * 4.21236379)] = $95,787.63. The amortization schedule shown below provides proof of the accuracy of the present value. Calculation of the effective interest rate using the formula: Y = [ 5,000 + ( 100,000.00 – 95,787.63 ) / 5 ] / ( 100,000.00 + 95,787.63 ) / 2 Y = 5,842.474 / 97,893.815 Y = 5.968172669 % ° Close to effective interest rate of 6.000% Amortization Schedule: Period Periodic Payment/ Receipt Actual Interest Amount Amortization Amount Value 0 95,787.63 1 5,000.00 747.26 96,534.89 2 5,000.00 792.09 97,326.98 3 5,000.00 839.62 98,166.60 4 5,000.00 890.00 99,056.60 5 5,000.00...
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