Question

P = $5000
r = 6.25%
Compounded daily for 5 years

Answer 1

Account balance = $6,834.01

Interest accrued = $1,834.01

Explanation:

To find the account balance of an initial investment of $5,000 at 6.25% compounded daily for 5 years, use the Compound Interest Formula.

Compound Interest Formula

`\large \text{$ \sf A=P\left(1+(r)/(n)\right)^(nt) $}`

where:

• A = Final amount.
• P = Principal amount.
• r = Interest rate (in decimal form).
• n = Number of times interest is applied per year.
• t = Time (in years).

As the interest is compounded daily, n = 365.

Therefore, the values to substitute into the formula are:

• P = $5,000
• r = 6.25% = 0.0625
• n = 365
• t = 5

Substitute the values into the formula and solve for A:

`\implies A=5000\left(1+(0.0625)/(365)\right)^(365 \cdot 5)`

`\implies A=5000\left(1.000171232...\right)^(1825)`

`\implies A=5000\left(1.3668013759...\right)`

`\implies A=6834.0068795...`

`\implies A=6834.01\; \sf (2\;d.p.)`

Therefore, the account balance after 5 years is $6,834.01, and the total amount of interest earned is $1,834.01.