GMAT Math help » Problem-Solving concerns » Word troubles » Interest problems » Calculating compound attention

Grandpa Jack wants to aid his grandson, tiny Jack, through college expenses. Tiny Jack is right now 3 year old. If Grandpa Jack invests \$5,000 in a university savings account earning 5% compounded yearly, exactly how much money will he have actually in 15 years when tiny Jack is 18?

Explanation:

To fix this, us can create an equation because that the value based on time. Therefore if we let t be the nmbers of years that have passed, we can create a role f(t) for the value in the to save account.

We note that f(0) =5000. (We invest 5000 in ~ time 0.) following year, the will have 5% more than that. To discover our complete value at the finish of the year, we multiply 5,000 * 1.05 = 5,250. F(1) = 5000(1.05)=5,250. In ~ the finish of year 2, us will have actually a 5% growth rate. In other words, f(2) = (1.05)* f(1). We deserve to rewrite this as . Us can start to watch the proper equation is . If we plugin t = 15, we will have our account balance at the end of 15 years. So, ours answer is .

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### Example inquiry #2 : Calculating Compound interest

Cherry invested dollars in a fund that payment 6% yearly interest, compounded monthly. I m sorry of the following represents the value, in dollars, the Cherry’s invest plus attention at the finish of 3 years?    Explanation:

The monthly price is 3 year = 36 month

According to the compound attention formula and here , , , so we have the right to plug right into the formula and also get the value Report one Error

### Example question #3 : Calculating Compound interest

Scott desires to invest \$1000 for 1 year. At bank A, his investment will certainly collect 3% interest compounded daily while at bank B, his investment will certainly collect 3.50% interest compounded monthly. Which bank offers a much better return? how much an ext will he get by selecting that financial institution over the other? Explanation:

Calculate the total amount from each bank using the complying with formula: Bank A: Bank B:  Report an Error

### Example inquiry #4 : Calculating Compound attention

Bryan invests \$8,000 in both a save account the pays 3% straightforward interest annually and also a certificate that deposit that pays 8% straightforward interest anually. ~ the very first year, Bryan has earned a full of \$365.00 from these investments. Exactly how much did Bryan invest in the certificate the deposit? Explanation:

Let be the amount Bryan invest in the certificate the deposit. Then he deposited in a save account. 8% that the quantity in the certificate that deposit is , and also 3% of the quantity in the save account is ; add these interest amounts to get \$365.00. Therefore, we can collection up and solve the equation:       Report an Error

### Example concern #5 : Calculating Compound interest

Barry invests \$9000 in corporate bonds at 8% annual interest, compounded quarterly. In ~ the end of the year, how much interest has actually his invest earned? Explanation:

Use the compound attention formula substituting (principal, or lot invested), (decimal equivalent of the 8% attention rate), (four soldier per year), (one year).   Subtract 9,000 indigenous this number - the attention earned is \$741.89

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### Example inquiry #6 : Calculating Compound attention

Tom deposits his \$10,000 inheritance in a to save account through a 4% annual interest rate, compounded quarterly. He pipeline it over there untouched for six months, after which that withdraws \$5,000. He leaves the remainder untouched for an additional six months.

How lot interest has Tom earn on the inheritance after one year? Explanation:

Since in each case the interest is compounded quarterly, the annual interest price of 4% is separated by 4 to gain 1%, the reliable quarterly interest rate.

The \$10,000 continues to be in the to save account 6 months, or 2 quarters, for this reason 1% is included twice - equivalently, the \$10,000 is multiply by 1.01 twice:  \$5,000 is withdrawn indigenous the to save account, leaving This money is untouched for six months, or 2 quarters, therefore again, us multiply by 1.01 twice:  Subtract \$5,000 to gain the interest: Report an Error

### Example concern #7 : Calculating Compound attention

On January 1, Gary borrows \$10,000 to purchase an automobile at 12% annual interest, compounded quarterly start on April 1. The agrees to pay \$800 per month ~ above the critical day of the month, beginning on January 31, over twelve months; his thirteenth payment, top top the complying with January 31, will certainly be the unpaid balance. Just how much will that thirteenth payment be? Explanation:

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

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

First quarter:  Second quarter:  Third quarter:  Fourth quarter:  The thriteenth payment, through which Gary will pay off the loan, will be \$913.16.

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### Example question #8 : Calculating Compound interest

Jessica deposits \$5,000 in a savings account at 6% interest. The interest is compounded monthly. Just how much will certainly she have in she savings account ~ 5 years?

None the the various other answers space correct. 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. Report one Error

### Example concern #9 : Calculating Compound interest

A actual estate firm is considering even if it is to accept a loan sell in bespeak to build property. The primary amount of the loan is \$400,000, and the annual interest price is 7% compounded semi-anually. If the firm accepts the loan, what will certainly be the balance after 4 years? Explanation:

Recall the formula for link interest: , wherein n is the variety of periods every year, r is the yearly interest rate, and also t is the variety of years.

Plug in the values offered in the question:  Report one Error

### Example concern #10 : Calculating Compound attention

Nick found a once-in-a-lifetime possibility to buy a rare arcade game being marketed at a garage sale for \$5730. However, Nick can"t bought that appropriate now, and also decides come take out a loan for \$1000. Nick didn"t really read the fine print on the loan, and also later figures out the the loan has a 30% annualy compounded attention rate! (A really dangerous rate). How much walk Nick owe on the loan 2 year from the moment he takes the end the loan? (Assume he"s lazy and doesn"t salary anything earlier over those 2 years.) Explanation:

For compound interest, the lot Nick owes is where is the principal, or starting amount the the loan (\$1000), is the interest rate per year (30% = .3). And is the moment that has passed because Nick took the end the loan. (2)

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