(a) $855 simple interest was paid when $4500 was invested at 4.75% per annum.Determine the period of investment.(b) Mrs. Woods borrowed a sum of money from a bank at 12.5% per annum for 6 yearsand paid $6375 simple interest. Calculate the sum of money mrs. Wood borrowedfrom the bank.(c) The simple interest on $15 000 for years is $4950. Calculate the rate percent perannum.
Question
(a) 4500 was invested at 4.75% per annum.Determine the period of investment.(b) Mrs. Woods borrowed a sum of money from a bank at 12.5% per annum for 6 yearsand paid 15 000 for years is $4950. Calculate the rate percent perannum.
Solution
(a) The formula for simple interest is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time. We can rearrange this formula to solve for T: T = I / (PR).
Given: I = 4500 R = 4.75% = 0.0475 (in decimal form)
Substituting these values into the formula, we get:
T = 855 / (4500 * 0.0475) = 4 years
So, the period of investment is 4 years.
(b) Using the same formula, we can rearrange it to solve for P: P = I / (RT).
Given: I = $6375 R = 12.5% = 0.125 (in decimal form) T = 6 years
Substituting these values into the formula, we get:
P = 6375 / (0.125 * 6) = $8500
So, Mrs. Woods borrowed $8500 from the bank.
(c) Again, using the same formula, we can rearrange it to solve for R: R = I / (PT).
Given: I = 15000 T = 4 years
Substituting these values into the formula, we get:
R = 4950 / (15000 * 4) = 0.0825
To convert this decimal to a percentage, we multiply by 100, so R = 0.0825 * 100 = 8.25%.
So, the rate of interest per annum is 8.25%.
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