simple interest\n1. renas grandfather opened a savings account as a college fund for her. his initial…
simple interest\n1. renas grandfather opened a savings account as a college fund for her. his initial deposit and the yearly simple - interest rate are shown. how much will rena have in this account after 2 years and 6 months?\n2. big money bank has an offer for new customers. if you deposit $5,000 in a savings account, you will earn 6.5% simple interest over the first 10 years.\na. how much interest will the account earn over this period?\nb. how much will be in the account after the 10 - year period?\nc. at the town savings bank, a new customer earns $2,950 in simple interest on a $5,000 deposit over the first 10 years. what rate of interest does that bank pay?\n3. dream loan bank offers loans. carrie borrows $10,500 to help start a business. the loan must be repaid at 4.5% simple interest over 10 years. how much money will carrie have to pay back?\n4. financial literacy kevin is going to open a savings account with $4,000. two different banks offer him two different options:\nbank a offers an account that will pay 6% simple interest for 6 years.\nbank b offers a special account for new customers that will pay 7% simple interest for 3 years. after the 3 years, kevin would have to transfer all his earnings to a regular account that will pay 5% simple interest on the new transferred principal.\nwhich offer will leave kevin with more money after 6 years? explain.
Answer
Explanation:
Step1: Recall simple - interest formula
The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. The total amount $A$ in an account is $A=P + I=P(1 + rt)$.
Step2: Solve problem 2A
Given $P = 5000$, $r=0.065$, and $t = 10$. First, find the interest $I$ using the formula $I=Prt$. $I=5000\times0.065\times10=3250$
Step2B: Solve problem 2B
The total amount $A$ in the account after 10 years is $A = P+I$. Substitute $P = 5000$ and $I = 3250$. $A=5000 + 3250=8250$
Step3: Solve problem 2C
Given $I = 2950$, $P = 5000$, and $t = 10$. Rearrange the simple - interest formula $I = Prt$ to solve for $r$. $r=\frac{I}{Pt}$ $r=\frac{2950}{5000\times10}=0.059 = 5.9%$
Step4: Solve problem 3
Given $P = 10500$, $r = 0.045$, and $t = 10$. First, find the interest $I$: $I=Prt=10500\times0.045\times10 = 4725$ The amount to be paid back $A=P + I$. $A=10500+4725 = 15225$
Step5: Solve problem 4 for Bank A
Given $P = 4000$, $r = 0.06$, and $t = 6$. Use the formula $A=P(1+rt)$. $A_A=4000\times(1 + 0.06\times6)=4000\times(1 + 0.36)=4000\times1.36 = 5440$
Step6: Solve problem 4 for Bank B
For the first 3 years: $P_1 = 4000$, $r_1=0.07$, $t_1 = 3$. $A_1=P_1(1 + r_1t_1)=4000\times(1+0.07\times3)=4000\times(1 + 0.21)=4000\times1.21 = 4840$ For the next 3 years: $P_2=4840$, $r_2 = 0.05$, $t_2 = 3$. $A_B=P_2(1 + r_2t_2)=4840\times(1+0.05\times3)=4840\times(1 + 0.15)=4840\times1.15=5566$
Since $5566>5440$, Bank B leaves Kevin with more money.
Answer:
2A. 3250 2B. 8250 2C. 5.9% 3. 15225 4. Bank B leaves Kevin with more money.