please do all parts in A-D. P5-3 (similar to) Question Hep Related to The Busine

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please do all parts in A-D.

P5-3 (similar to) Question Hep 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 $18,000. You intend to use your inheritance as a down payment on your house ce in an ccount that eams 7 percent interest compounded annually, how many years ill it be before your inheritance grows to 535,000? b. If you let your money grow for 10.5 years at 7 percent, how much will you have? Hlow lang will t take your money to grow to $35,000 if you move t into an account that pays 4 percent compounded annually? How long will t take your money to grow to $35,000 if you move it into an account that pays 11 percent? d. What does all this tell you about the relationiship among interest rates, time, and future sums? a. If you put your inheritance in an account that eans 7 percent interest compounded annually, how many years will i be before your inheritance grows to $35,000? years (Round to one decimal place) Enter your answer in the answer box and then click Check Answer Clear All O Type here to search 28 PM

Explanation / Answer

Answer a.

Present Value = $18,000
Future Value = $35,000
Interest Rate = 7%

Let $18,000 will grow to $35,000 in ‘n’ years

Present Value * (1+ Interest Rate)^Period = Future Value
$18,000 * 1.07^n = $35,000
1.07^n = 1.9444
n * ln(1.07) = ln(1.9444)
n = ln(1.9444) / ln(1.07)
n = 9.8 years

So, it will take 9.8 years for inheritance to growth to $35,000

Answer b.

Present Value = $18,000
Interest Rate = 7%
Period = 10.50 years

Future Value = Present Value * (1 + Interest Rate)^Period
Future Value = $18,000 * 1.07^10.50
Future Value = $36,627.07

Answer c.

If Interest Rate is 4%:

Present Value = $18,000
Future Value = $35,000
Interest Rate = 4%

Let $18,000 will grow to $35,000 in ‘n’ years

Present Value * (1+ Interest Rate)^Period = Future Value
$18,000 * 1.04^n = $35,000
1.04^n = 1.9444
n * ln(1.04) = ln(1.9444)
n = ln(1.9444) / ln(1.04)
n = 17.0 years

So, it will take 17.0 years for inheritance to growth to $35,000

If Interest Rate is 11%:

Present Value = $18,000
Future Value = $35,000
Interest Rate = 11%

Let $18,000 will grow to $35,000 in ‘n’ years

Present Value * (1+ Interest Rate)^Period = Future Value
$18,000 * 1.11^n = $35,000
1.11^n = 1.9444
n * ln(1.11) = ln(1.9444)
n = ln(1.9444) / ln(1.11)
n = 6.4 years

So, it will take 6.4 years for inheritance to growth to $35,000

Answer d.

If Present Value and Future Value remain constant:
If interest rate increases, then time will decrease.
If interest rate decreases, then time will increase.

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