Manhattan FDP | Percents : Problem Set : Q5)

[xerocoool]

Hi Tommy,

Q) A 7% car loan, which is compounded annually, has an interest payment of $210 after the first year. What is the principal on the loan ?

Why does the Compound Interest formula fail to work in this case. The interest amount at the end of 1st year for both Simple Interest and Compound Interest (annual compounding) is the same right ? So if we backtrack, the principal amount should be same (I assume)

Simple Interest -

SI = P * R * T
210 = P * 7/100 * 1
21000/7 = P
P = 3,000

CI = P (1+R/N)^nt (n=1,t=1)
210 = P (1+0.07)^1
210 = P (1.07)
P = 196.26 (approx 197)


Thanks
xero

[asishkm]

Hi xero,

In the formula related to Compound Interest:

A = P(1+ R/N)^Nt

A is the total amount and NOT the compound interest

The CI = A - P = P(1 + R/N)^(Nt) - P

[xerocoool]

hey,

yes, A = P(1+r/n)^nt

but A = amount + interest right ?

[asishkm]

Hi Xero,

A = Amount = Principal + Interest
=> Interest = A - Principal = A - P

and since A = P(1+R/N)^NT, Interest = P(1 + R/n)^nT - P

In the question, you are given the value of the "Interest"

Here t=1, n = 1, r = 0.07

So, 210 = P(1 + 0.07)^1 - P = 0.07P

=> P = 210/0.07 = 3000

Note: It is worth noting that if T = 1, (and it is compounded annually) then the total interest (compound) = the simple interest

[tommywallach]

I'm gonna kill you guys!

You keep overcomplicating questions. You don't need the compound interest formula if it's compounded annually! You only need it if it's compounded in some lesser amount of time.

Don't overthink questions! It'll kill you on test day!

-t