You are hoping to buy a house in the future and recently received an inheritance

Question

You are hoping to buy a house in the future and recently received an inheritance of $24,000. You intend to use your inheritance as a down payment on your house. If you put your inheritance in an account that earns 7 percent interest compounded annually, how many years will it be before your inheritance grows to $35,000? If you let your money grow for 10.25 years at 7 percent, how much will you have? How long will it take your money to grow to $35,000 if you move it into an account that pays 3 percent compounded annually? How long will it take your money to grow to $35,000 if you move it into an account that pays 13 percent? What does all this tell you about the relationship among interest rates, time, and future sums? If you put your inheritance in an account that earns 7 percent interest compounded annually, how many years will it be before your inheritance grows to $35,000? years (Round to one decimal place.) If you let your money grow for 10.25 years at 7 percent, how much will you have? (Round to the nearest cent.)

Explanation / Answer

Answer a.

Let n be the time in which $24,000 grow to $35,000 with interest rate 7%.

24,000*1.07^n = 35,000

N = 5.58 years

Answer b.

24,000*1.07^10.25 = $48,017

Answer c.

Let n be the time in which $24,000 grow to $35,000 with interest rate 3%.

24,000*1.03^n = 35,000

N = 12.76 years

Let n be the time in which $24,000 grow to $35,000 with interest rate 13%.

24,000*1.13^n = 35,000

N = 3.09 years

Answer d.

If the interest rate increase then the fund take less time to achieve the expected future sum.

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