Interest, Annuities, and Amortization.
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Please provide the formulas and 2 solved examples using the formulas for each of these topics:
Simple interest
Compound interest
Future value of an annuity
Present value of an annuity
Amortization
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Solution Summary
This solution is comprised of detailed explanation and step-by-step calculation of Simple interest, Compound interest, Future value of an annuity, Present value of an annuity, and Amortization.
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Please provide the formulas and 2 solved examples using the formulas for each of these topics:
Simple interest (I) = Prt
Where:
P is the principal amount
r is the annual rate
t is the time in years.
Examples:
1. Suppose you locate a two-year investment that pays 14% per year. If you invest $325, how much of this is simple interest?
I = Prt = (325) (0.14) (2) = $91.
2. Mary invest $4,000 for 3 years at 5% per year. How much of this is the simple interest?
I = Prt = (4,000) (0.05) (3) = $600.
Compound interest:
A = P (1 + r)n
Total interest earned: A - P.
Therefore, compound interest is total interest - simple interest.
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal (the initial amount you borrow or deposit).
r is the annual rate of interest (percentage).
n is the number of years the amount is deposited or borrowed for.
Examples:
1. In the previous example (number 1), how much is compound interest?
A = 325 (1 + 0.14)2 = $422.37
Total interest earned: $422.37 - $325 = $97.37
Therefore, compound interest is $97.37 - $91 = $6.37
2. In the previous example (number 2), how much is compound interest?
A = 4,000 (1 + 0.05)3 = $4630.50
Total interest earned: $4630.50 - $4,000 = $630.50
Therefore, compound interest is $630.50 - $600 = $30.50
Future value of an annuity (FVAN) = PMT [((1 + I)N - 1) / I]
Where:
PMT is the annual fixed payment.
I is the ...
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