(Related to The Business of Life: Saving for Your First House) (Future value) Yo

Question

(Related to The Business of Life: Saving for Your First House) (Future value) You are hoping to buy a house in the future and recently received an inheritance of $22,000. You intend to use your inheritance as a down payment on your house. 3. a. If you put your inheritance in an account that earns 8 percent interest compounded annually, how many years will it be before your inheritance grows to $33,000? b. If you let your money grow for 9.75 years at 8 percent, how much will you have? c. How long will it take your money to grow to $33,000 if you move it into an account that pays 5 percent compounded annually? How long will it take your money to grow to $33,000 if you move it into an account that pays 11 percent? d. What does all this tell you about the relationship among interest rates, time, and future sums? a. If you put your inheritance in an account that eams 8 percent interest compounded annually, how many years will it be before your inheritance grows to $33,000? years (Round to one decimal place.) b. If you let your money grow for 9.75 years at 8 percent, how much will you have? Round to the nearest cent.) c. How long wllit take your money to grow to $33,000 if you move it into an account that pays 5 percent compounded annually? years (Round to one decimal place.) How long will it take your money to grow to $33,000 if you move it into an account that pays 11 percent? years (Round to one decimal place.) d. What does all this tell you about the relationship among interest rates, time, and future sums? There is a (1) relationship between both the interest rate used to compound a present sum and the number of years for which the compounding continues and the future value of that sum, (Select from the drop-down menu.) (1) O positive O negative

Explanation / Answer

a. To calculate the time period, we can use following formula

FV = PV * (1+i) ^n

Where, FV is the future value = $33,000

Present Value (PV) =$22,000

i = I/Y = interest rate per year = 8%

And n is time period =?

Therefore,

$33,000 = $22,000 * (1+8%) ^n

$33,000/ $22,000 = (1+8%) ^n

Or n = 5.3 years

It will take 5.3 years to grow money to $33,000.

b. To calculate the Future value, we can use following formula

FV = PV * (1+i) ^n

Where, FV is the future value =?

Present Value (PV) =$22,000

i = I/Y = interest rate per year = 8%

And n is time period =9.75

Therefore,

FV = $22,000 * (1+8%) ^9.75

= $46,591.24

c. To calculate the time period, we can use following formula

FV = PV * (1+i) ^n

Where, FV is the future value = $33,000

Present Value (PV) =$22,000

i = I/Y = interest rate per year = 5%

And n is time period =?

Therefore,

$33,000 = $22,000 * (1+5%) ^n

$33,000 /$22,000 = (1+5%) ^n

Or n = 8.3 years

It will take 8.3 years to grow money to $33,000 at 5% interest rate

And if i = I/Y = interest rate per year = 11%

Therefore,

$33,000 = $22,000 * (1+11%) ^n

$33,000 /$22,000 = (1+11%) ^n

Or n = 3.9 years

It will take 3.9 years to grow money to $33,000 at 11% interest rate

d. There is a positive relationship between both the interest rate used to compound the present sum and number of years for which the compounding continues the future value of that sum.

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