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

$23,392

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

Answer 2

The principal amount was $23,393.45

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+(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+(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 =
`(98000)/(4.189386)`

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45