Math of Money:Compound Interest Review With Applications

Math of Money:Compound Interest Review With Applications

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Compound Interest:

The value that is futureFV) of a good investment of present 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) mt or

where i = r/m is the interest per compounding period and n = mt is the true wide range of compounding periods.

You can re solve for the value that is present to acquire:

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

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

Realize that the attention earned 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 only one time each year. In this context r can be called the nominal price, and it is frequently denoted as r nom .

Numerical instance: A CD spending 9.8% compounded month-to-month includes 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 obtain a fruitful interest of 10.25per cent, considering that the compounding makes the CD paying 9.8% compounded month-to-month really pay 10.25% interest during the period of the entire year.

Mortgage repayments elements: allow where P = principal, r = interest per period, n = quantity of periods, k = quantity of re payments, R = payment that is monthly and D = financial obligation stability after K re payments, then

R = P Р§ r / [1 – (1 + r) -n ]

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

Accelerating Mortgage Payments Components: Suppose one chooses to spend a lot more than the payment per month, the real question is just how many months can it just simply just take before the mortgage is paid down? The solution is, the rounded-up, where:

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

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

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

FV = [ R(1 + r) letter – 1 ] / r

Future Value for an Increasing Annuity: it really is a good investment that is making interest, and into which regular re re payments of a set amount are built. Suppose one makes a repayment of R at the conclusion of each compounding period into a good investment with something special value of PV, repaying interest at a yearly price of r compounded m times each year, then a future value after t years should be

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

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

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 a decade, how much money into the account is:

FV = PV(1 i that is + 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 12 months to readiness, we = the attention price, D = the dividend, and F = the face-value at the conclusion of N years, then worth of the relationship is V, where

V = (D/i) + (F – D/i)/(1 + i) letter

V could be the amount of the worthiness regarding the dividends in addition to payment that is final.

You’d like to perform some sensitiveness analysis when it comes to “what-if” scenarios by entering different numerical value(s), in order to make your “good” strategic choice.

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  • Periodic Compound Interest
  • Compound Interest’s Factors
  • Compound Interest & Good Speed
  • Mortgage Repayments
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  • Accelerating Mortgage Repayments
  • Future Value of a Annuity
  • When Will Your Pension Money Run Out?
  • Just exactly What must be the Present Value of the Bond You Need?
  • Your Loan’s Payment Per Month
  • Pension Planner’s Calculator
  • Buying/Selling Shares with Commissions
  • Substitute the present example that is numerical with your own personal case-information, and then click one the determine .