name date 2 - 5 compound interest formula exercises round to the nearest cent wherever necessary. 1. mr…

name date 2 - 5 compound interest formula exercises round to the nearest cent wherever necessary. 1. mr. mady opens a savings account with principal p dollars that pays 2.11% interest compounded quarterly. express his ending balance after one - year algebraically. 2. jeff deposits $2,300 at 1.13% interest compounded weekly. what will be his ending balance after one year? 3. nancy has $4,111 in an account that pays 1.07% interest compounded monthly. what is her ending balance after two years? 4. mr. weinstein has a savings account with a balance of $19,211.34. it pays 1.1% interest compounded daily. what is his ending balance after three years, if no other deposits or withdrawals are made? how much interest does he earn over the three years? 5. if you invested $10,000 at 3.8% compounded hourly for five years, what would be your ending balance? 6. danielle has a cd at crossland bank. she invests $22,350 for four years at 1.55% interest, compounded monthly. what is her ending balance? how much interest did she make? 7. ms. santoro is opening a one - year cd for $16,000. the interest is compounded daily. she is told by the bank representative that the annual percentage rate (apr) is 1.8%. what is the annual percentage yield (apy) for this account? 8. knob hill savings bank offers a one - year cd at 1.88% interest compounded daily. what is the apy for this account? round to the nearest hundredth of a percent. 9. kings park bank is advertising a special 1.66% apr for cds. kevin takes out a one - year cd for $24,000. the interest is compounded daily. find the apy for kevins account. 10. imagine that you invest $100,000 in an account that pays 5.9% annual interest compounded monthly. what will your balance be at the end of 18 years? 11. yurik invests $88,000 in a cd that is locked into a 1.75% interest rate compounded monthly, for seven years. how much will yurik have in the account when the cd matures?

Answer

Explanation:

Step1: Recordar fórmula de interés compuesto

La fórmula de interés compuesto es $A = P(1+\frac{r}{n})^{nt}$, donde $A$ es el saldo final, $P$ es el capital inicial, $r$ es la tasa de interés anual (en decimal), $n$ es el número de veces que se capitaliza el interés por año y $t$ es el número de años.

Step2: Resolver ejercicio 1

Para el Sr. Mady, $P$ es el capital inicial, $r = 0.0211$ (2.11% en decimal), $n = 4$ (compuesto trimestralmente) y $t = 1$. Entonces $A = P(1+\frac{0.0211}{4})^{4\times1}=P(1 + 0.005275)^{4}=P(1.005275)^{4}$.

Step3: Resolver ejercicio 2

Para Jeff, $P=$2300$, $r = 0.0113$ (1.13% en decimal), $n = 52$ (compuesto semanalmente) y $t = 1$. $A = 2300(1+\frac{0.0113}{52})^{52\times1}=2300(1+\frac{0.0113}{52})^{52}\approx2300(1 + 0.0002173)^{52}\approx2300\times1.01137\approx$2326.15$.

Step4: Resolver ejercicio 3

Para Nancy, $P = 4111$, $r=0.0107$ (1.07% en decimal), $n = 12$ (compuesto mensualmente) y $t = 2$. $A=4111(1+\frac{0.0107}{12})^{12\times2}=4111(1+\frac{0.0107}{12})^{24}\approx4111\times1.0216\approx$4199.89$.

Step5: Resolver ejercicio 4

Para el Sr. Weinstein, $P = 19211.34$, $r = 0.011$ (1.1% en decimal), $n = 365$ (compuesto diariamente) y $t = 3$. $A=19211.34(1+\frac{0.011}{365})^{365\times3}=19211.34(1+\frac{0.011}{365})^{1095}\approx19211.34\times1.0337\approx$19859.79$. El interés ganado es $I=A - P=19859.79 - 19211.34=$648.45$.

Step6: Resolver ejercicio 5

Para una inversión de $P = 10000$, $r = 0.038$ (3.8% en decimal), $n = 24$ (compuesto horariamente) y $t = 5$. $A=10000(1+\frac{0.038}{24})^{24\times5}=10000(1+\frac{0.038}{24})^{120}\approx10000\times1.2099\approx$12099$.

Step7: Resolver ejercicio 6

Para Danielle, $P = 22350$, $r = 0.0155$ (1.55% en decimal), $n = 12$ (compuesto mensualmente) y $t = 4$. $A=22350(1+\frac{0.0155}{12})^{12\times4}=22350(1+\frac{0.0155}{12})^{48}\approx22350\times1.0641\approx$23782.64$. El interés ganado es $I=A - P=23782.64 - 22350=$1432.64$.

Step8: Resolver ejercicio 7

La tasa efectiva anual (APY) se calcula con la fórmula $APY=(1+\frac{r}{n})^{n}-1$, donde $r = 0.018$ (1.8% en decimal) y $n = 365$ (compuesto diariamente). $APY=(1+\frac{0.018}{365})^{365}-1=(1 + 0.0000493)^{365}-1\approx1.0182 - 1=0.0182$ o $1.82%$.

Step9: Resolver ejercicio 8

Para Knob Hill Savings Bank, $r = 0.0188$ (1.88% en decimal) y $n = 365$. $APY=(1+\frac{0.0188}{365})^{365}-1=(1+0.0000515)^{365}-1\approx1.0190 - 1 = 0.0190$ o $1.90%$.

Step10: Resolver ejercicio 9

Para Kings Park Bank, $r = 0.0166$ (1.66% en decimal) y $n = 365$. $APY=(1+\frac{0.0166}{365})^{365}-1=(1 + 0.0000455)^{365}-1\approx1.0167 - 1=0.0167$ o $1.67%$.

Step11: Resolver ejercicio 10

Para una inversión de $P = 100000$, $r = 0.059$ (5.9% en decimal), $n = 12$ (compuesto mensualmente) y $t = 18$. $A=100000(1+\frac{0.059}{12})^{12\times18}=100000(1+\frac{0.059}{12})^{216}\approx100000\times2.8574\approx$285740$.

Step12: Resolver ejercicio 11

Para Yurik, $P = 88000$, $r = 0.0175$ (1.75% en decimal), $n = 12$ (compuesto mensualmente) y $t = 7$. $A=88000(1+\frac{0.0175}{12})^{12\times7}=88000(1+\frac{0.0175}{12})^{84}\approx88000\times1.1317\approx$99589.60$.

Answer:

$A = P(1.005275)^{4}$
$$2326.15$
$$4199.89$
Saldo final: $$19859.79$, Interés ganado: $$648.45$
$$12099$
Saldo final: $$23782.64$, Interés ganado: $$1432.64$
$1.82%$
$1.90%$
$1.67%$
$$285740$
$$99589.60$