Question 1: A man invested GH¢2400.00 at an interest rate of 7% per year. At the end of a certain period, the principal and interest together amounted to GH¢2456.00. How long was the money invested? Question 2: Patience invested GH¢90.00 for 2 years at $r$% per year simple interest. At the end of 2 years, the amount of money she has is GH¢99. Calculate the value of $r$.

1. Problem Description

Question 1: A man invested GH¢2400.00 at an interest rate of 7% per year. At the end of a certain period, the principal and interest together amounted to GH¢2456.

0

0. How long was the money invested?

Question 2: Patience invested GH¢90.00 for 2 years at $r$% per year simple interest. At the end of 2 years, the amount of money she has is GH¢

9

9. Calculate the value of $r$.

2. Solution Steps

Question 1:

The simple interest formula is:

$I = PRT$

where:

$I$ is the simple interest

$P$ is the principal amount

$R$ is the interest rate (as a decimal)

$T$ is the time in years.

We are given:

$P = 2400$

$R = 7\% = 0.07$

The final amount is $2456$, so the interest earned is $I = 2456 - 2400 = 56$.

Now, we can plug these values into the simple interest formula and solve for $T$:

$56 = 2400 \times 0.07 \times T$

$56 = 168T$

$T = \frac{56}{168}$

$T = \frac{1}{3}$

Question 2:

The simple interest formula is:

$I = PRT$

where:

$I$ is the simple interest

$P$ is the principal amount

$R$ is the interest rate (as a decimal)

$T$ is the time in years.

We are given:

$P = 90$

$T = 2$

The final amount is $99$, so the interest earned is $I = 99 - 90 = 9$.

Now, we can plug these values into the simple interest formula and solve for $R$:

$9 = 90 \times R \times 2$

$9 = 180R$

$R = \frac{9}{180}$

$R = \frac{1}{20}$

$R = 0.05$

Since $R$ is in percentage, we have $r = 0.05 \times 100 = 5$.

3. Final Answer

Question 1: The money was invested for $\frac{1}{3}$ year.

Question 2: The value of $r$ is 5.