Question

can you help me with these problems i have been trying many time , but no luck and I don't know what step that I miss can you show the steps please

Thanks

1. 3 year(s) ago, Goran invested 32,251 dollars. He has earned and will earn 8.54 percent per year in compound interest. If Sarah invests 49,680 dollars in 3 year(s) from today and earns simple interest, then how much simple interest per year must Sarah earn to have the same amount of money in 8 years from today as Goran will have in 8 years from today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

and this one too

2 year(s) ago, Fatima invested 6,210 dollars. In 2 year(s) from today, she expects to have 7,520 dollars. If Fatima expects to earn the same annual return after 2 year(s) from today as the annual rate implied from the past and expected values given in the problem, then in how many years from today does she expect to have exactly 10,350 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).  

Answer 1

1.

The total number of years for which Goran invested is 11.

The future value of goran investment is calculated below:

Future value = 32, 251 x (1 +0.0854)11

Future value = 32,251 x 2.46313372

Future value = 79, 438.5256

The simple interest earned by sarah is calculated below:

49, 680 X (1+ix 5) = 79, 438.5256

(1+ix 5) = 1.599

(ix 5) = 0.599

i = 0.1198

The simple interest rate is 0.1198.

2.

Annual rate earned by fatima is calculated below:

6, 210 (1 + i)4 = 7,520

(1+i)4 = 1.21095

(1 + i) = 1.210957

(1+i) = 1.049

i = 0.049

The time at which account reaches to 10,350 from starting time is calculated below:

6,210 x (1 + 0.049) = 10,350

(1+0.049) = 1.66667

Take log on both sides

nlog (1 + 0.049) = log1.66667

log1.66667 log (1 + 0.049)

n = 10.68

Thus, from today, it will take (10.68 - 2) = 8.68 years to reach 10,350.