Q5)
Selima deposits $5000 ( t = 0 years) in an account paying r(2) = 3.00%.At the end of 4 years (t = 4 years) she adds another $9000 to her account and the interest rate changes to r(2) = X%. After another 3 years ( t = 7 years) she adds another $7000 to her account and the interest changes to r(2) = 3.00%. At the end of 11 years, she has $27567.44 in her account.
a) How much money does she have in her account at t = 4 years just before she makes her deposit?
b) How much money does she have in her account after 7 years, just after she makes her deposit?
c) What is X%?
Deposit at t0 =$5000
FV at end of 4 years= 5000*(1+3%)^4=5000*1.03^4=5000*1.1255=$5627.54
Total amount at emd of 4 years=5627.54+9000=$14627.54
FV at the end of 7 years=14627.54*(1+x)^3
Total amount at the end of 7 years=14627.54*(1+x)^3+7000
FV at the end of 11 years=(14627.54*(1+x)^3+7000)*(1+3%)^4
Or, 27567.44=(14627.54*(1+x)^3+7000)*1.03^4
Or, 14627.54*(1+x)^3+7000=27567.44/1.1255
Or, 14627.54*(1+x)^3=24493.31-7000
Or, (1+x)^3=17493.31/14627.44
Or, 1+x=1.1959^(1/3)
Or,x=1.0615-1
Or,x=0.0615 or 6.15%
Amswer a: Amount at end of 4 year=$5627.54
Answer b: Amount at end of 7 years=5627.54*(1+6.15%)^3=5627.54*1.1959=$6730.98
Amount after deposit =6730.98+7000=$13730.98
Answer c:x=6.15%
Get Answers For Free
Most questions answered within 1 hours.