Math of Money:Compound Interest Review With Applications

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Compound Interest:

The value that is futureFV) of a good investment of current value (PV) bucks making interest at a yearly price of r compounded m times each year for a time period of t years is:

FV = PV(1 r/m that is + mt or

where i = r/m is the interest per compounding period and n = mt is the true amount of compounding durations.

You can re re re solve when it comes to present value PV to acquire:

Numerical Example: For 4-year investment of $20,000 making 8.5% each year, with interest re-invested every month, the future value is

FV = PV(1 r/m that is + mt = 20,000(1 + 0.085/12) (12)(4) = $28,065.30

Realize that the attention won is $28,065.30 – $20,000 = $8,065.30 — significantly more compared to matching easy interest.

Effective Interest price: If cash is spent at a rate that is annual, compounded m times each year, the effective rate of interest is:

r eff = (1 r/m that is + m – 1.

Here is the rate of interest that will provide the exact same yield if compounded just once each year. In this context r can also be called the nominal price, and it is frequently denoted as r nom .

Numerical instance: A CD spending 9.8% compounded month-to-month has a nominal price of r nom = 0.098, plus a rate that is effective of

r eff =(1 + r nom /m) m = (1 + 0.098/12) 12 – 1 = 0.1025.

Therefore, we have a fruitful rate of interest of 10.25per cent, because the compounding makes the CD having to pay 9.8% compounded month-to-month really pay 10.25% interest during the period of the entire year.

Home loan repayments elements: allow where P = principal, r = interest per period, n = quantity of periods, k = wide range of payments, R = monthly repayment, and D = debt stability after K re re re payments, then

R = P Р§ r / [1 – (1 + r) -n ]

D = P Р§ (1 + r) k – R Р§ [(1 + r) k – 1)/r]

Accelerating Mortgage Payments Components: Suppose one chooses to spend significantly more than the payment that is monthly the real question is exactly how many months does it just simply take before the home loan is paid down? The clear answer is, the rounded-up, where:

n = log[x / (x – P Ч r)] / log (1 + r)

where Log could be the logarithm in virtually any base, state 10, or ag ag e.

Future Value (FV) of a Annuity Components: Ler where R = re re re payment, r = interest rate, and n = wide range of re re payments, then

FV = [ R(1 + r) letter – 1 ] / r

Future Value for the Increasing Annuity: it really is an investment this is certainly making interest, and into which regular re payments of a hard and fast amount are produced. Suppose one makes a repayment of R at the conclusion of each compounding period into an investment with a present-day worth of PV, repaying interest at a yearly price of r compounded m times each year, then your future value after t years is supposed to be

FV = PV(1 + i) n + [ R ( (1 + i) n – 1 ) ] / i

where i = r/m could be the interest compensated each period and letter = m Р§ t may be the final number of durations.

Numerical instance: You deposit $100 per thirty days into an account that now contains $5,000 and earns 5% interest each year compounded month-to-month. After ten years, how much money into the account is:

FV = PV(1 + i) n + [ R(1 + i) letter – 1 ] / i = 5,000(1+0.05/12) 120 + [100(1+0.05/12) 120 – 1 ] / (0.05/12) = $23,763.28

Worth of a relationship: allow N = quantity of to maturity, I = the interest rate, D = the dividend, and F = the face-value payday loans Minnesota at the end of N years, then the value of the bond is V, where year

V = (D/i) + (F – D/i)/(1 + i) letter

V may be the amount of the worth for the dividends and also the payment that is final.

You’d like to perform some sensitivity analysis for the “what-if” situations by entering different numerical value(s), to create your “good” strategic choice.

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  • Home Loan Repayments
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  • Accelerating Mortgage Repayments
  • Future Value of a Annuity
  • Whenever Will Your Retirement Money Run Out?
  • Exactly just exactly What must be the Present Value of a Bond You Need?
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    Math of Money:Compound Interest Review With Applications

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