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Ike is buying a motorcycle. To save for his down payment, he invests
$3750 to for 5 years at
6.4% compounded quarterly. At the end of 5 years how much will lke have saved? (3 marks)

$3$ . Ike is buying a motorcycle. To save for his down payment, he invests $\$ 3750$ to for $5$ years at $6.4 \%$ compounded quarterly. At the end of $5$ years how much will lke have saved? ( $3$ marks)

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Finance problems

Full solution

Q.

3

. Ike is buying a motorcycle. To save for his down payment, he invests

\$ 3750

to for

5

years at

6.4 \%

compounded quarterly. At the end of

5

years how much will lke have saved? (

3

marks)

Identify formula for compound interest: Identify the formula for compound interest: $A = P(1 + \frac{r}{n})^{(nt)}$ . Here, $A$ is the amount of money accumulated after $n$ years, including interest. $P$ is the principal amount (the initial amount of money). $r$ is the annual interest rate (decimal). $n$ is the number of times that interest is compounded per year. $t$ is the time the money is invested for in years.
Convert annual interest rate: Convert the annual interest rate from a percentage to a decimal by dividing by $100$ . $\newline$ $6.4\% = \frac{6.4}{100} = 0.064$ .
Plug values into formula: Plug the values into the formula. $\newline$ $P = \$3750$ , $r = 0.064$ , $n = 4$ (because interest is compounded quarterly), and $t = 5$ . $\newline$ $A = 3750(1 + \frac{0.064}{4})^{(4\cdot5)}$ .
Calculate values and exponent: Calculate the values inside the parentheses and the exponent. $\newline$ $1 + \frac{0.064}{4} = 1 + 0.016 = 1.016$ . $\newline$ Now raise $1.016$ to the power of $20$ (because $4\times5 = 20$ ). $\newline$ $A = 3750 \times 1.016^{20}$ .
Calculate $1.016^{20}$ : Calculate $1.016^{20}$ using a calculator. $\newline$ $1.016^{20} \approx 1.34885$ (rounded to five decimal places).
Multiply principal amount: Multiply the principal amount by the result from step $5$ . $\newline$ $A = 3750 \times 1.34885$ . $\newline$ $A \approx 5058.19$ .

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