Question

Juana deposited 5300.00 into a savings account that compounded intorest sembanmualy. What nominal anrual fale compounded tomi-annualy was eamed on the investment it the bidance was $482.80 in three years? The nominal annual rate of interest is % per annum compounded sems-annually. (Round the firzal answer to four decimal places as needed. Round al intermediate values to six decimal places as needed.)

Answer 1

2.64

Step-by-step explanation:

* Juana deposited $5,300.00 into a savings account

* The interest was compounded semiannually

* After 3 years, the balance was $4,827.80

* We need to find the nominal annual rate of interest

* To find the interest rate:

* Let r be the nominal annual interest rate

* With semiannual compounding, the effective rate per 6 month period is r/2

* After 6 months, the balance is 5300(1 + r/2)

* After 1 year, the balance is 5300(1 + r/2)^2

* After 1.5 years, the balance is 5300(1 + r/2)^3

* After 2 years, the balance is 5300(1 + r/2)^4

* After 2.5 years, the balance is 5300(1 + r/2)^5

* After 3 years, the balance is 5300(1 + r/2)^6 = 4827.80

* Solving this:

* 5300(1 + r/2)^6 = 4827.80

* (1 + r/2)^6 = 0.911698

* 1 + r/2 = 0.98677 (taking the 6th root)

* r/2 = 0.98677 - 1 = -0.01323

* r = -0.01323 * 2 = 0.0264

* The nominal annual interest rate is 2.64%

Therefore, the nominal annual rate of interest compounded semiannually is 2.6400%.

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