Question

13. You expect to receive OMR 11,500 at graduation in 3 years. You plan on investing this money at 8 percent compounded semi-annually until you have OMR 75,000. How many years from now will it be until this occurs?

Answer 1

Given

amount to be invested =  OMR 11,500

interest rate = 8%

total future value OMR 75,000

let time be t

using future value formula FV= PV *(1+ r/2)^2t

note: compounded semi annualy implies 2 payments each year

75000 = 11500 * (1+ 0.08/2)^2t

75000 = 11500 * 1.04^2t

6.5217=1.04^2t

taking natural logarith on both sides

ln (6.5217) = ln (1.04^2t)

ln (6.5217) = 2t *ln (1.04)

1.8751 = 2t *0.0392

2t = 47.83 = 48

t = 48/2 = 24

so it will take around 24 years

given that 11,500 is receievd after 3 years of graduation

so from today it will take 24 years +3 years for amount to become OMR 75,000

So from now it will take 27 years to reach the amount of OMR 75,000