Question

Yvonne bought a car for $10,300. After 3 years, the value of the car was $6,250. The value of this car decreases exponentially over time. In approximately what number of additional months will the value of Yvonne’s car be 50% of the price she originally paid?

Answer 1

Answer:

A = $44,778.84

A = P + I where

P (principal) = $10,300.00

I (interest) = $34,478.84 or 12 months

Step-by-step explanation:

Given: Yvonne bought a car for $10,300. After 3 years, the value of the car was $6,250. 50%

To find: In approximately what number of additional months will the value of Yvonne’s car be 50% of the price she originally paid?

Formula: $(\frac{interest rate}{number of payments})$ × $loan principal = interest$

Solution:  Divide your interest rate by the number of payments you’ll make in the year (interest rates are expressed annually). So, for example, if you’re making monthly payments, divide by 12. Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.

(This gives you the amount of interest you pay the first month.)

First, convert R as a percent to r as a decimal

r = R/100

r = 50/100

r = 0.5 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,300.00(1 + 0.5/12)(12)(3)

A = 10,300.00(1 + 0.041666667)(36)

A = $44,778.84

Henceforth:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,300.00 at a rate of 50% per year compounded 12 times per year over 3 years is $44,778.84.