Stanford Simmons, who recently sold his Porsche, placed $10,000 in a savings account paying annual compound interest of 6%. A.) Calculate the amount of money that will have accrued if he leaves the money in the bank for 1, 5, and 15 years. B.) If he moves his money into an account that pays 8% or one that pays 10%, rework part (a) using these new interest rates. C.) What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you have completed in this problem?

When the rate of interest is held constant but the time for the loan is increased, the future sum increases. Where the interest rate is increased , the future amount value rises as long as the principal amount and time span are held constant .

Explanation:

A. The formula to apply here is that of compound interest;

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where ;

A=Final amount

P=Initial principal amount

r=Interest rate

n=number of times interest is applied in a period

t=time periods elapsed

Given;

P=$10,000 r=6% t=1 or 5 or 15 years, n=1 ,

A=$10,000(1+0.06)^1 = $10,000(1.06)^1 =$ 10600

A=$10000(1+0.06)^5 = $10,000(1.06)^5 =$13382.26

A=$10000(1+0.06)^15=$10,000(1.06)^15 =$23965.58

B. Moving the money into an account which pays 8% and 10% the amount will be;

A=$10,000(1+0.08)^1 = $10,000(1.08)^1 =$10800

A=$10,000(1+0.08)^5=$10,000(1.08)^5=$14693.28

A=$10,000(1+0.08)^15=$10,000(1.08)^15=$31721.69

A=$10,000(1+0.1)^1 = $10,000(1.1) =$11000

A=$10,000(1+0.1)^5=$10,000(1.1)^5=$16105.10

A=$10,000(1+0.1)^15=$10,000(1.1)^15=$41772.48

C.When interest rate is increased , the future amount value rises as long as the principal amount and time span is held constant .This is evident from the values calculated in the three cases.When the rate of interest is held constant but the time for the loan is increased, the future sum increases. When the principal amount is the same but both the interest rate and time for loan increased, the sum of future amount increases.