Question

Calculate the nominal rate of interest p.a. compounded semi-annually if $5000.00 accumulates to $7002.64 in 78 months.

Select one:
a. 2.625%
b. 0.02625%
c. 0.0525%
d. 5.25%
e. 0,8656%

Answer 1

The nominal rate of interest p.a. compounded semi-annually is approximately(d) 5.25%.

Step-by-step explanation:

To calculate the nominal rate of interest compounded semi-annually, we can use the compound interest formula:

`\[A = P \left(1 + (r)/(n)\right)^(nt)\]`

Where:

`\(A\)` is the future value of the investment
`(\$7002.64),`

`\(P\)`is the principal amount
`(\$5000.00),`

`\(r\)` is the nominal interest rate per compounding period (what we need to find),

`\(n\)` is the number of times interest is compounded per year (2 for semi-annual),

`\(t\)` is the time the money is invested for in years (78 months converted to years is
`\(78/12\)).`

Rearranging the formula to solve for
`\(r\)`, we get:

`\[r = n\left(\left((A)/(P)\right)^{(1)/(nt)} - 1\right)\]`

Substituting the given values:

`\[r = 2\left(\left((7002.64)/(5000.00)\right)^{(1)/(2 * 78/12)} - 1\right)\]`

After performing the calculations, the nominal rate of interest (\(r\)) is approximately 0.0525, or 5.25%. Therefore, the correct answer is option (d) 5.25%. This indicates that, when compounded semi-annually, the investment grows from $5000.00 to $7002.64 over the 78-month period at an annual nominal interest rate of 5.25%.