Question

The total amount paid on a 35 year loan was $98,000. If the interest rate was 4.1% and compounded monthly, what was the principal? Round your answer to the nearest cent.

Answer 1

Answer:

The principal amount was $23,393.45

Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

$A=P(1+\frac{r}{n})^{nt}$

Where A = amount (98,000)

           P = Principal amount (P)

           r = rate of interest 4.1% (0.041)

           n = number of compounding interest monthly (12)

           t = time (35 years)

$98,000=P(1+\frac{0.041}{12})^{(12)(35)}$

$98,000=P(1+0.003416)^{(420)}$

$98,000=P(1.003416)^{(420)}$

98,000 = P(4.189386)

= 4.189386P = 98,000

P = $\frac{98000}{4.189386}$

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45

Answer 2

Answer:

$23,392

Step-by-step explanation:

Use the compound interest formula and substitute the values given: $98,000=P(1+.041/12)$^{12(35)}$

Simplify using order of operations:

$98,000=P(1.003416667)$^{420}$

P=$98,000(1.003416667)$^{420}$

P≈$23,392