Asked by Lauren-Nicole Caday on Jun 07, 2024

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If $4,000 is to be paid now. What amount would be equivalent 97 days earlier given an interest rate of 4.25% per year?

A) $3,955.33
B) $3,844.22
C) $3,733.11
D) $3,622.00
E) $4,421.67

Interest Rate

The portion of a loan subject to interest fees for the borrower, typically indicated as an annual percentage of the remaining loan principal.

Paid Now

A term indicating an immediate payment or settlement of a transaction.

  • Learn the concept of value equivalence across distinct time phases, considering the impact of the interest rate.
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gagan chahalJun 10, 2024
Final Answer :
A
Explanation :
To find the equivalent amount 97 days earlier, we use the formula for calculating the present value: PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}PV=(1+r)nFV , where PVPVPV is the present value, FVFVFV is the future value ($4,000), rrr is the interest rate per period (4.25% per year or 0.0425), and nnn is the number of periods. Since the interest rate is annual, we convert 97 days into years by dividing by 365: n=97365n = \frac{97}{365}n=36597 . Plugging the values into the formula gives: PV=4000(1+0.0425)97365PV = \frac{4000}{(1 + 0.0425)^{\frac{97}{365}}}PV=(1+0.0425)365974000 , which calculates to approximately $3,955.33.