Use the equation $=$0*(1 + r)xn
where $ is the amount of money, $0 is the initial amount of money, r is the rate, x is the number of times per year the interest is compounded, and n is the number of years the interest is compounded. We are solving for n. To do this we need to use logs.
log(1 + r)($/$0)/x = n
log1.08(5006/1000)/12 = n = 1.744 years.
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With the same rate of interest, monthly compounding is more than 3 times as large.The ratio of the logarithms of capital+interest is 3.
Simple interest (compounded once) Initial amount(1+interest rate) Compound Interest Initial amount(1+interest rate/number of times compounding)^number of times compounding per yr
An effective annual interest rate considers compounding. When the principle is compounded multiple times each year the interest rate increased to be more than the stated interest rate. The increased interest rate is the effective annual interest rate.
Yes: a year is not 50 weeks.
No. If the account is earning interest the current amount should be greater than the initial deposit.
Compound Interest FormulaP = principal amount (the initial amount you borrow or deposit)r = annual rate of interest (as a decimal)t = number of years the amount is deposited or borrowed for.A = amount of money accumulated after n years, including interest.n = number of times the interest is compounded per yearExample:An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. What is the balance after 6 years?Solution:Using the compound interest formula, we have thatP = 1500, r = 4.3/100 = 0.043, n = 4, t = 6. Therefore, So, the balance after 6 years is approximately $1,938.84.
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Four.
Once.
Equivalent RatesThe Equivalent Rates calculation is used to find the nominal annual interest rate compounded n times a year equivalent to a given nominal rate compounded m times per year.Two nominal rates with different compounding frequencies are equivalent if they yield the same amount of interest per year (and hence, at the end of any period of time).Input• nominal annual rate for the given rate• compounding frequency for the given rate• compounding frequency for the equivalent rateResults• equivalent nominal annual rate• equivalent periodic rateExample•A bank offers 14.75 % compounded annually.What would be the equivalent rate compounded monthly?InputGiven nominal annual rate:14.75 %Compounding frequency for given rate:annuallyCompounding frequency for equivalent rate:monthlyResultEquivalent nominal annual rate:13.8377 %Answer: 13.8377%.
"Compounded annually" means that the interest is added once a year.
The more times that interest is compounded the more growth of savings.
A=P(1+r/n)^nt. where P is the initial principal deposited in an account that pays interest at annual rate r(expressed as a decimal), compounded n times per year. the amount after t years.