Find the amount and interest after 3 years if compound interest at 5 is charged on sum of ₹ 4000

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

FV = PV(1 + r/m)mtor

FV = PV(1 + i)n

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

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

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

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

Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.

Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1 + rnom /m)m   =   (1 + 0.098/12)12 - 1   =  0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P � r / [1 - (1 + r)-n]

D = P � (1 + r)k - R � [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

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

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

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be

FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i where i = r/m is the interest paid each period and n = m � t is the total number of periods.

Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

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

Value of a Bond:

V is the sum of the value of the dividends and the final payment.

You may like to perform some sensitivity analysis for the "what-if" scenarios by entering different numerical value(s), to make your "good" strategic decision.

Replace the existing numerical example, with your own case-information, and then click one the Calculate.

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Grandpa Jack wants to help his grandson, Little Jack, with college expenses. Little Jack is currently 3 years old. If Grandpa Jack invests $5,000 in a college savings account earning 5% compounded yearly, how much money will he have in 15 years when Little Jack is 18? 

Possible Answers:

 Between $11,000-$11,500 

 Between $9,000-$9,500 

Between $10,000-$10,500

 Between $9,500-$10,000 

 Between $10,500-$11,000 

Correct answer:

Between $10,000-$10,500

Explanation:

To solve this, we can create an equation for the value based on time. So if we let t be the nmbers of years that have passed, we can create a function f(t) for the value in the savings account. 

We note that f(0) =5000. (We invest 5000 at time 0.) Next year, he will have 5% more than that. To find our total value at the end of the year, we multiply 5,000 * 1.05 = 5,250. f(1) = 5000(1.05)=5,250. At the end of year 2, we will have a 5% growth rate. In other words, f(2) = (1.05)* f(1). We can rewrite this as  . We can begin to see the proper equation is 

Cherry invested  dollars in a fund that paid 6% annual interest, compounded monthly. Which of the following represents the value, in dollars, of Cherry’s investment plus interest at the end of 3 years?

Correct answer:

Explanation:

The monthly rate is 

3 years = 36 months

According to the compound interest formula

and here , , , so we can plug into the formula and get the value

Scott wants to invest $1000 for 1 year. At Bank A, his investment will collect 3% interest compounded daily while at Bank B, his investment will collect 3.50% interest compounded monthly. Which bank offers a better return? How much more will he receive by choosing that bank over the other?

Correct answer:

Explanation:

Calculate the total amount from each bank using the following formula:

Bank A:

Bank B:

Bryan invests $8,000 in both a savings account that pays 3% simple interest annually and a certificate of deposit that pays 8% simple interest anually. After the first year, Bryan has earned a total of $365.00 from these investments. How much did Bryan invest in the certificate of deposit?

Correct answer:

Explanation:

Let  be the amount Bryan invested in the certificate of deposit. Then he deposited  in a savings account. 8% of the amount in the certificate of deposit is , and 3% of the amount in the savings account is ; add these interest amounts to get $365.00.  Therefore, we can set up and solve the equation:

Barry invests $9000 in corporate bonds at 8% annual interest, compounded quarterly. At the end of the year, how much interest has his investment earned?

Correct answer:

Explanation:

Use the compound interest formula

substituting  (principal, or amount invested),  (decimal equivalent of the 8% interest rate),  (four quarters per year),  (one year).

Subtract 9,000 from this figure - the interest earned is $741.89

Tom deposits his $10,000 inheritance in a savings account with a 4% annual interest rate, compounded quarterly. He leaves it there untouched for six months, after which he withdraws $5,000. He leaves the remainder untouched for another six months.

How much interest has Tom earned on the inheritance after one year?

Correct answer:

Explanation:

Since in each case the interest is compounded quarterly, the annual interest rate of 4% is divided by 4 to get 1%, the effective quarterly interest rate. 

The $10,000 remains in the savings account six months, or two quarters, so 1% is added twice - equivalently, the $10,000 is multiplied by 1.01 twice:

$5,000 is withdrawn from the savings account, leaving 

This money is untouched for six months, or two quarters, so again, we multiply by 1.01 twice:

Subtract $5,000 to get the interest:

On January 1, Gary borrows $10,000 to purchase an automobile at 12% annual interest, compounded quarterly beginning on April 1. He agrees to pay $800 per month on the last day of the month, beginning on January 31, over twelve months; his thirteenth payment, on the following January 31, will be the unpaid balance. How much will that thirteenth payment be?

Correct answer:

Explanation:

12% annual interest compounded quarterly is, effectively, 3% interest per quarter.

Over the course of one quarter, Gary pays off , and the remainder of the loan accruses 3% interest. This happens four times, so we will subtract $2,400 and subsequently multiply by 1.03 (adding 3% interest) four times. 

First quarter:

Second quarter:

Third quarter:

Fourth quarter:

The thriteenth payment, with which Gary will pay off the loan, will be $913.16.

Jessica deposits $5,000 in a savings account at 6% interest. The interest is compounded monthly. How much will she have in her savings account after 5 years?

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

where  is the principal,  is the number of times per year interest is compounded,  is the time in years, and  is the interest rate.

A real estate company is considering whether to accept a loan offer in order to develop property.  The principal amount of the loan is $400,000, and the annual interest rate is 7% compounded semi-anually. If the company accepts the loan, what will be the balance after 4 years?

Correct answer:

Explanation:

Recall the formula for compound interest:

, where n is the number of periods per year, r is the annual interest rate, and t is the number of years.

Plug in the values given in the question:

Nick found a once-in-a-lifetime opportunity to buy a rare arcade game being sold at a garage sale for $5730. However, Nick can't afford that right now, and decides to take out a loan for $1000. Nick didn't really read the fine print on the loan, and later figures out that the loan has a 30% annualy compounded interest rate! (A very dangerous rate). How much does Nick owe on the loan 2 years from the time he takes out the loan? (Assume he's lazy and doesn't pay anything back over those 2 years.)

Correct answer:

Explanation:

For compound interest, the amount Nick owes is

where  is the principal, or starting amount of the loan ($1000),  is the interest rate per year (30% = .3). and  is the time that has passed since Nick took out the loan. (2)

We have

Hence our answer is $1690.

All GMAT Math Resources

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