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Mr. X is to invest Rs. 100000 every year for the next 5 years (at the beginning of the period) @ 5%. How much he would have at the end of the 5-year period?
a. 508191
b. 508911
c. 580191
d. 580911
Ans - c
Solution:
P = 1000000, R = 5% p.a., T = 5 Y
This question asks the FUTURE VALUE OF INVESTMENT AT THE BEGINNING OF PERIOD, so, FVAD (Future Value of Annuity Due) is applied.
The formula of FVAD =
-----------------------------------------------------
FVAD = (C ÷ R) x { (1 + R)^T - 1 } x (1 + R)
-----------------------------------------------------
So,
FVAD = (100000÷0.05) x {{1+0.05}^5 – 1} x (1 + 0.05)
= 2000000 x (1.2763 - 1) x (1.05)
= 2000000 x 0.2763 x 1.05
= 552563 × 1.05
= 580191
So, he would have Rs. 580191 at the end of the 5th year.
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Mr. X is to invest Rs. 150000 at the beginning of each year for 4 years @ 10% ROI. How much amount he will receive at the end of 4 years?
a. 1237076
b. 1273076
c. 1630772
d. 1673072
Ans - b
Solution:
P = 1500000
R = 10% p.a.
T = 6 Y
This question asks the FUTURE VALUE OF INVESTMENT AT THE BEGINNING OF PERIOD, so, FVAD (Future Value of Annuity Due) is applied.
The formula of FVAD =
-----------------------------------------------------
FVAD = (C ÷ R) x { (1 + R)^T - 1 } x (1 + R)
-----------------------------------------------------
So,
FVAD = (150000÷0.1) x {{1+0.1}^6 – 1} x (1 + 0.1)
= 1500000 x (1.7716 - 1) x (1.1)
= 1500000 x 0.7716 x 1.1
= 1157342 x 1.1
= 1273076
So, he will receive Rs. 1273076 at the end of 6 years.
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Mr. X wants to send his daughter to a management school after 5 years and will need onetime payment of charges amounting to Rs. 7 lac. At 12% ROI, how much he should invest annually (at the beginning of each year)?
a. 93881
b. 98381
c. 110186
d. 111086
Ans - b
Hint:
Use FVAD formula to find C. Here FV is given.
This question asks the FUTURE VALUE OF INVESTMENT AT THE BEGINNING OF PERIOD, so, FVAD (Future Value of Annuity Due) is applied.
The formula of FVAD =
-----------------------------------------------------
FVAD = (C ÷ R) x { (1 + R)^T - 1 } x (1 + R)
-----------------------------------------------------
So,
700000 = (x ÷ 0.12) * {{1+0.12}^5 – 1} * (1+0.12)
700000 = (x ÷ 0.12) * (1.7623 - 1) * (1+0.12)
700000 = (x ÷ 0.12) * 0.7623 * 1.12
918223 = x ÷ 0.12 * 1.12
819842 = x ÷ 0.12
819842 * 0.12 = x
98381 = x
So, he should invest Rs. 98381 annually at the beginning of each year.
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How much money will a student owe at graduation if she borrows Rs. 3000 (at the beginning of each year) per year @ 5% interest during each of her 4 years of school?
a. 12390
b. 12930
c. 13577
d. 13755
Ans - c
Hint:
Use FVAD formula to find FV. Here C is given.
This question asks the FUTURE VALUE OF INVESTMENT AT THE BEGINNING OF PERIOD, so, FVAD (Future Value of Annuity Due) is applied.
The formula of FVAD =
-----------------------------------------------------
FVAD = (C ÷ R) x { (1 + R)^T - 1 } x (1 + R)
-----------------------------------------------------
So,
FVAD = (3000÷0.05) * {{1+0.05}^4 – 1} * (1+0.05)
= 60000 * (1.2155 - 1) * 1.05
= 60000 * 0.2155 * 1.05
= 12930 * 1.05
= 13577
So, the student owe Rs. 13577 at graduation
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