Question

Buck is planning to save $63.65 every six months for 7 years. He plans to make his first savings contribution later today. If he currently has $423.73 saved and expects to have $2,125.26 in 7 years from today, then what is the EAR that he expects to earn? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Information provided:

Semi-annual saving= $63.65

Time= 7 years*2= 14 semi-annual periods

Present value= $423.73

Future value= $2125.26

The question is solved by first calculating the yield to maturity.

Enter the below in a financial calculator to compute the yield to maturity:

PMT= 63.65

N= 14

PV= -423.73

FV= 2125.26

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 21.2061.

Therefore, the yield to maturity is 21.2061/2= 10.6030% 10.60%.

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1+0.1060/2)^2-1

        = 1.1088-1

        = 0.1088*100= 10.88%

Therefore, the effective annual rate is 10.88%.

In case of any query, kindly comment on the solution.