analyzing interest scenarios within personal finance contexts to make informed decisions\nrory needs a…

analyzing interest scenarios within personal finance contexts to make informed decisions\nrory needs a $10,000 loan for education. lender x offers 5% compound interest compounded annually, while lender y offers 6% simple interest. if rory plans to repay in 4 years, which lender should he choose to minimize interest?\ncompound interest formula: $a = p(1+\frac{r}{n})^{nt}$\nsimple interest formula: $a = p(1 + rt)$\nunable to determine\nlender x with 5% compound interest\nlender y with 6% simple interest\ninterest cost same at both lenders

analyzing interest scenarios within personal finance contexts to make informed decisions\nrory needs a $10,000 loan for education. lender x offers 5% compound interest compounded annually, while lender y offers 6% simple interest. if rory plans to repay in 4 years, which lender should he choose to minimize interest?\ncompound interest formula: $a = p(1+\frac{r}{n})^{nt}$\nsimple interest formula: $a = p(1 + rt)$\nunable to determine\nlender x with 5% compound interest\nlender y with 6% simple interest\ninterest cost same at both lenders

Answer

Explanation:

Step1: Calculate total amount for Lender X

For compound - interest formula $A = P(1 + r)^t$, where $P=$10000$, $r = 0.05$, and $t = 4$. $A_X=10000\times(1 + 0.05)^4=10000\times1.05^4=10000\times1.21550625=$12155.0625$. Interest paid $I_X=A_X - P=12155.0625 - 10000=$2155.0625$.

Step2: Calculate total amount for Lender Y

For simple - interest formula $A = P(1+rt)$, where $P = 10000$, $r = 0.06$, and $t = 4$. $A_Y=10000\times(1+0.06\times4)=10000\times(1 + 0.24)=$12400$. Interest paid $I_Y=A_Y - P=12400 - 10000=$2400$.

Step3: Compare the interests

Since $I_X=$2155.0625$ and $I_Y=$2400$, and $I_X<I_Y$.

Answer:

B. Lender X with 5% compound interest