The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan's simple interest rate, r, to the nearest tenth of a percent.
P=$130, A=171.60, T=4 years
To find the simple interest rate (r), we can use the formula:
\(A = P(1 + rt)\)
where A is the future value, P is the principal, r is the interest rate, and t is the time period.
First, let's rearrange the formula to solve for r:
\(r = \frac{{A - P}}{{Pt}}\)
Plug in the given values:
\(P = \$130\), \(A = \$171.60\), and \(t = 4\) years
\(r = \frac{{171.60 - 130}}{{130 \times 4}}\)
\(r = \frac{{41.60}}{{520}}\)
\(r \approx 0.08\) or 8% (rounded to the nearest tenth of a percent)
Therefore, the loan's simple interest rate is approximately 8%.
To determine the loan's simple interest rate, we can use the formula for simple interest:
I = P * r * t,
where:
- I represents the interest accrued on the loan
- P is the principal borrowed
- r is the interest rate
- t is the time in years
In this case, we have the principal P = $130, the future value A = $171.60, and the time T = 4 years. We need to calculate the interest rate r.
Rearranging the formula, we have:
r = (A - P) / (P * t)
Substituting the given values, we get:
r = (171.60 - 130) / (130 * 4)
r ≈ 41.60 / 520
r ≈ 0.08 or 8%
Therefore, the loan's simple interest rate to the nearest tenth of a percent is 8.0%.
171.6 = 130 + 4*130*r
41.6 = 520 r
r = .08 = 8%