Compound Interest problems
- 1. Two payments of $10,000 each must be made one year and four years from now. If money can earn 9% compounded monthly, what single payment two years from now would be equivalent to the two scheduled payments?
Options- A. 19296
- B. 19396
- C. 19496
- D. 19596 Also asked in: Bank Exams, Bank PO
Correct Answer: 19296
Explanation:
The single equivalent payment will be PV + FV.
FV = Future value of $10,000, 12 months later
$10,000 *(1.0075)/12
$10,938.07
PV= Present value of $10,000, 24 months earlier
$10,000/(1.0075)24
$8358.31
The equivalent single payment is
$10,938.07 + $8358.31 = $19,296.38
- 2. A chartered bank offers a five-year Escalator Guaranteed Investment Certificate.In successive years it pays annual interest rates of 4%, 4.5%, 5%, 5.5%, and 6%, respectively, compounded at the end of each year. The bank also offers regular five-year GICs paying a fixed rate of 5% compounded annually. Calculate and compare the maturity values of $1000 invested in each type of GIC. (Note that 5% is the average of the five successive one-year rates paid on the Escalator GIC.)
Options- A. 1276.28
- B. 1234
- C. 1278
- D. 1256 Also asked in: Bank Exams, Bank PO
Correct Answer: 1276.28
Explanation:
FV = $1000(1.04)(1.045)(1.05)(1.055)(1.06) = $1276.14
the maturity value of the regular GIC is
FV = $ 1000 x = $1276.28
- 3. If the rate of inflation for the next 20 years is 2.5% per year, what annual income will be needed 20 years from now to have the same purchasing power as a $30,000 annual income today?
Options- A. 39158
- B. 49158
- C. 59158
- D. 69158 Also asked in: Bank Exams, Bank PO
Correct Answer: 49158
Explanation:
i=j/m
FV = PV(1+ i)^n
- 4. Payments of $2000 and $1000 were originally scheduled to be paid one year and five years, respectively, from today. They are to be replaced by a $1500 payment due four years from today, and another payment due two years from today. The replacement stream must be economically equivalent to the scheduled stream. What is the unknown payment, if money can earn 7% compounded semiannually?
Options- A. 1548
- B. 1348
- C. 1648
- D. 1748 Also asked in: Bank Exams, Bank PO
Correct Answer: 1648
Explanation:
FV1 = Future value of $2000, 1 year later
= PV (1+ i)^n
- 5. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 1155. The simple interest on the same sum for double the time at half the rate percent per annum is ?
Options- A. Rs. 1100
- B. Rs. 5500
- C. Rs. 1400
- D. Rs. 4120 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: Rs. 1100
Explanation:
Let the sum be Rs.x. Then,
=> x =5500
sum = Rs. 5500.
So, S.I = Rs. = 1100
- 6. In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly ?
Options- A. Quarter months
- B. Half year
- C. 2 years
- D. 1 year Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: Half year
Explanation:
3300 ----- 3% ? (1st time interval, 99) ? 3399.
Here, time interval is given as half-yearly i.e. 6 months.
- 7. If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.
Options- A. Rs.1251
- B. Rs.1261
- C. Rs.1271
- D. Rs,1281 Also asked in: Bank Exams, Bank PO
Correct Answer: Rs.1261
Explanation:
Clearly, Rate = 5% p.a .,
Time = 3 years
S.I =Rs.1200.
So,Principal
=Rs.(100 x 1200/3x5)
=Rs.8000.
Amount
=Rs.[8000 x (1+5/100)³]
=Rs(8000x21/20x21/20x21/20)
= Rs.9261
C.I
=Rs.(9261-8000)
=Rs.1261.
- 8. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is
Options- A. 2years
- B. 3years
- C. 4years
- D. 5years Also asked in: Bank Exams, Bank PO
Correct Answer: 2years
- 9. What will be compounded amount? I. Rs. 200 was borrowed for 192 months at 6% compounded annually. II. Rs. 200 was borrowed for 16 years at 6%.
Options- A. I alone sufficient while II alone not sufficient to answer
- B. II alone sufficient while I alone not sufficient to answer
- C. Either I or II alone sufficient to answer
- D. Both I and II are not sufficient to answer Also asked in: Bank Exams, Bank PO
Correct Answer: Either I or II alone sufficient to answer
Explanation:
I. Amount =
II. Amount =
Thus, I as well as II gives the answer.
- 10. Find the effective rate of interest for an investment that earns 5 1/2% per year, compounded continuously
Options- A. 5.65%
- B. 5.75%
- C. 5.85%
- D. 5.95% Also asked in: Bank Exams, Bank PO
Correct Answer: 5.65%
Explanation:
We are not given a value of P in this problem, so either pick a value
for P and stick with that throughout the problem, or just let P = P.
We have that t = 1, and r = .055. To find the effective rate of interest,
first find out how much money we have after one year:
A = Pert
A = Pe(.055)(1)
A = 1.056541P.
Therefore, after 1 year, whatever the principal was, we now have 1.056541P.
Next, find out how much interest was earned, I, by subtracting the initial amount of money from the final amount:
I = A ? P
= 1.056541P ? P
= .056541P.
Finally, to find the effective rate of interest, use the simple interest formula, I = Prt. So,
I = Pr(1) = .056541P
.056541 = r.
Therefore, the effective rate of interest is 5.65%
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