How long would it take a construction loan for $548,048 to earn interest of $50,000 at 9% exact interest?
Answer (2)
Use the simple interest formula: I = P v er tt .
Plug in the given values: 50000 = 548048 v er t 0.09 v er tt .
Solve for t in years: t = 548048 v er t 0.09 50000 ≈ 1.0137 years.
Convert to days using exact interest: t d a ys = 1.0137 × 365 ≈ 370 days. The final answer is 370 days .
Explanation
Understanding the Problem We are given a construction loan of $548,048 that earns interest of $50,000 at an exact interest rate of 9%. We need to find out how long it would take for the loan to earn that much interest.
Recalling the Simple Interest Formula The formula for simple interest is: I = P v er tt where:
I is the interest earned,
P is the principal amount (the initial loan amount),
r is the annual interest rate (as a decimal),
t is the time in years.
Identifying the Given Values We are given:
P = $548 , 048
I = $50 , 000
r = 9% = 0.09 We need to find t .
Substituting the Values Plug the given values into the formula: 50000 = 548048 v er t 0.09 v er tt
Calculating Time in Years Now, solve for t :
t = 548048 v er t 0.09 50000 t = 49324.32 50000 t ≈ 1.0137 years
Calculating Time in Days Since we need to find the time in days and we are using exact interest, we multiply the time in years by 365: t d a ys = 1.0137 × 365 ≈ 370 days
Final Answer Therefore, it would take approximately 370 days for the construction loan to earn $50,000 in interest.
Examples
Understanding how long it takes for an investment to grow is crucial in financial planning. For instance, if you invest $10,000 in a savings account with a 5% annual interest rate, you can calculate how long it will take to earn 1 , 000 inin t eres t . T hi sc a l c u l a t i o nh e lp syo u pl an f or f u t u ree x p e n ses , se t f inan c ia l g o a l s , an d mak e in f or m e dd ec i s i o n s ab o u t yo u r in v es t m e n t s . K n o w in g t h e t im e i tt ak es f oryo u r m o n ey t o g ro w a ll o w syo u t o a l i g n yo u r in v es t m e n t s w i t h yo u r f inan c ia lt im e l in e an d n ee d s . T h es im pl e in t eres t f or m u l a I = P vert t$ is a fundamental tool for such calculations.
It would take approximately 370 days for the construction loan of $548,048 to earn $50,000 in interest at a rate of 9%. This is calculated using the simple interest formula to solve for time. The final calculation shows that this time period corresponds to just over one year.
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