Deck 10: Compound Interest - Further Topics

Question 1

In how many years will money double at 6.62% compounded semi-annually?

Answer 1

PV = 1, FV = 2, i = 0.0662÷2 = 0.0331
n = = = = 21.28569
The number of years = = 10.64 years

Question 2

A financial obligation requires the payment of $250.00 in eighteen months, $350.00 in thirty months, and $300.00 in fifty-four months. When can the obligation be discharged by a single payment of $800.00 if interest is 5% compounded semi-annually?

Answer 2

Let the focal date be now; i = 0.05÷2 = 0.025; m = 2
For the obligation:
250.00(1.025)-3 + 350.00(1.025)-5 + 300.00(1.025)-9
250.00(.928599411) + 350.00(.883854288) + 300.00(.800728362)
232.15 + 309.35 + 240.22 = 781.72
For the payment: 800(1.025)-n
n = = = = 0.93611429 (semi-annual) ÷ 2×12 = 5.62 months
Programmed solution:

Question 3

A financial obligation requires the payment of $1000.00 in nine months, and $500.00 in twelve months. When can the obligation be discharged by a single payment of $1700.00 if interest is 12% compounded quarterly?

Answer 3

Let the focal date be now; i = 0.12÷4 = 0.03; m = 4
Debts = 1000.00(1.03)-3 +500.00(1.03)-4 = 1359.38
FV = 1700, PV = 1359.38
n = = = = 7.56456693 quarters
= 1.891141733 years
The discharge date is 1 year 325 days from now.

Question 4

A six-year, $1650.00 note bearing interest at 9.51% compounded annually was discounted at 11.2% compounded semi-annually yielding proceeds of $1916.75. How many months before the due date was the discount date?

Question 5

Find the equated date at which two payments of $1600.00 due six months ago and $1850.00 due today could be settled by a payment of $4300.00 if interest is 9.48% compounded monthly.

Question 6

A five-year, $4500.00 promissory note with interest at 7.5% compounded semi-annually was discounted at 8% compounded quarterly yielding proceeds of $6150.00. How many months before the due date was the discount date?

Question 7

A financial obligation requires the payment of $1500.00 in nine months, $700.00 in twenty-one months, and $1700.00 in 33 months. When can the obligation be discharged by a single payment of $3900.00 if interest is 8.44% compounded quarterly?

Question 8

A loan of $9000.00 was repaid together with interest of $3728.00. If interest was 9.4% compounded quarterly, how long was the loan taken out? (Give answer in years and months to the nearest tenth)

Question 9

A 11-year $8000.00 promissory note, with interest at 8.4% compounded monthly, is discounted at 6.5% compounded semi-annually yielding proceeds of $14 631.15. How many months before the due date was the date of discount?

Question 10

In how many months will money double at 7.45% compounded semi-annually?

Question 11

A loan of $4500.00 was repaid together with interest of $1164.00. If interest was 12 .4% compounded quarterly, for how many months was the loan taken out?

Question 12

A five-year, $2000.00 note bearing interest at 10% compounded annually was discounted at 12% compounded semi-annually yielding proceeds of $1900.00. How many months before the due date was the discount date?

Question 13

A financial obligation requires payments of $2000.00 today, $2500.00 in three years, and $3000.00 in five years. When can the obligation be discharged by a single payment equal to the sum of the required payments if interest is 6%p.a. compounded monthly?

Question 14

In how many days will $770.00 grow to $880.00 at 11.5% p.a. compounded monthly?

Question 15

A promissory note for $3600.00 dated May 15, 2012, requires an interest payment of $370.00 at maturity. If interest is at 9.6% compounded monthly, determine the due date of the note.

Question 16

Calculate the number of years for money to triple at 3.6% p.a. compounded monthly.

Question 17

Luciano sold a property and is to receive $14200.00 in nine months, $14000.00 in 42 months, and $15500.00 in 57 months. The deal was renegotiated after six months at which time Luciano received a payment of $17000.00; he was to receive a further payment of $19000.00 later. When should Luciano receive the second payment if money is worth 10% compounded quarterly?

Question 18

Janice owes two debt payments, a payment of $6700 due in twelve months and a payment of $8750 due in twenty-one months. If Janice makes a payment of $7000 now, when should she make a second payment of $7900 if money is worth 11.5% compounded semi-annually?

Question 19

In how many years will money triple at 12% compounded semi-annually?

Question 20

At what nominal rate of interest compounded semi-annually will $11 800 earn $6 800 interest in six years?

Question 21

Calculate the nominal annual rate of interest compounded quarterly that is equivalent to 10% p.a. compounded semi-annually.

Question 22

If $1400.00 accumulates to $2350.00 in five years, six months compounded semi-annually, what is the effective rate of interest?

Question 23

What is the nominal rate of interest at which money will triple itself in eight years and six months if compounded semi-annually?

Question 24

A principal of $4250.00 compounded monthly amounts to $4800.00 in 6.25 years. What is the nominal annual rate of interest?

Question 25

If the effective rate of interest on an investment is 7%, what is the nominal rate of interest compounded quarterly?

Question 26

In how many years will money triple at 6.4% compounded monthly?

A) 206.53 years
B) 17.71 years
C) 17.21 years
D) 1.48 years
E) 2.57 years

Question 27

The accountant of Crystal Credit Union proposes changing the method of compounding interest on premium savings accounts to yearly compounding. If the current rate is 8% compounded quarterly, what nominal rate should the treasurer suggest to the Board of Directors to maintain the same effective rate of interest?

Question 28

At what nominal rate of interest compounded semi-annually will $5900 earn $6400 interest in six years?

Question 29

Determine the effective rate of interest corresponding to 6% p.a. compounded monthly

Question 30

At what nominal rate of interest compounded quarterly will $8100 earn $1700.00 interest in six years?

Question 31

Calculate the nominal rate of interest compounded semi-annually that is equivalent to 8.4% compounded monthly.

Question 32

What is the nominal rate of interest compounded semi-annually which is equivalent to an effective rate of 5.89%?

Question 33

At what nominal rate of interest compounded quarterly will $2000.00 earn $400.00 interest in three years?

Question 34

If the effective rate of interest on an investment is 6.52%, what is the nominal rate of interest compounded monthly?

Question 35

What is the nominal rate of interest compounded semi-annually that is equivalent to an effective rate of 8.25%

Question 36

A principal of $5000.00 compounded monthly amounts to $6000.00 in 7 years. What is the nominal annual rate of interest?

Question 37

At what nominal rate of interest compounded monthly will $1700.00 earn $500.00 interest in three years?

Question 38

The treasurer of Lynn Lake Credit Union proposes changing the method of compounding interest on premium savings accounts to daily compounding. If the current rate is 4% compounded quarterly, what nominal rate should the treasurer suggest to the Board of Directors to maintain the same effective rate of interest?

Question 39

At what nominal rate of interest compounded annually will $5000 earn $2500 interest in seven years?

Question 40

Calculate the nominal rate of interest compounded semi-annually that will double money in eight years.

Question 41

How long, in compounding periods, will it take for $3327 to increase by $3799 if you are able to earn 6.2% compounded semi-annually?

A) 42.95
B) 24.95
C) 4.56
D) 6.45
E) 4.95

Question 42

At what nominal rate of interest compounded quarterly will $ 13 000,00 earn $8407.27 in interest in six years? (nearest hundredth)

A) 1.83%
B) 2.10%
C) 7.33%
D) 8.4%
E) 18.4%

Question 43

What nominal rate of interest-compounded quarterly will have to be earned on a savings account for it to grow from $1525 to $1955 over a period of 21 months?

A) 14.45%
B) 15.45%
C) 12.45%
D) 3.61%
E) 10.45%

Question 44

Deon has $4000.00 invested at 4.5% compounded semi-annually at her bank. In order to make a comparison with another financial institution she needs to know the effective rate of interest at her bank. What is the effective annual rate of interest?

A) 1.12%
B) 2.28%
C) 9.10%
D) 4.55%
E) 4.5%

Question 45

What is the quarterly interest rate that you will need to earn in order for an investment of $1635 to grow to be $1748.73 after 2.25 years?

A) 12.93%
B) 13.93%
C) 10.93%
D) 8.93%
E) 3.00%

Question 46

How many compounding periods does it take for a non-interest bearing bond of $420150 to be reduced to $199989 at a discount rate of 5.44% compounded monthly?

A) 146.12
B) 121.12
C) 154.12
D) 184.12
E) 164.12

Question 47

How long did it take for $1635 to increase to $2310 if the investment earned interest at a rate of 8.08% compounded quarterly (give your final answer in years and months, e.g., 3 years and 7.23 months)?

A) 7 years 7.69 months
B) 4 years .64 months
C) 3 years 4.79 months
D) 4 years 3.84 months
E) 8 years 1.69 months

Question 48

Calculate the effective annual rate for 5% p.a. compounded semi-annually.

A) 0.050625
B) 5.0625%
C) 0.0255%
D) 2.55%
E) 15.0625%

Question 49

Calculate the effective annual rate for 10% p.a. compounded quarterly.

A) 0.1038%
B) 1.038%
C) 10.38%
D) 10%
E) 2.5%

Question 50

In how many years will money double at 8% compounded yearly?

A) 0.09 years
B) 0.9 years
C) 9.01 years
D) 90.1 years
E) 2 years

Question 51

What is the monthly discount rate expressed as an nominal annual rate for a future value of $182500 to be reduced to $178,663.58 over a period of 4.25 years?

A) 4.06%
B) 8.04%
C) 6.88%
D) 4.88%
E) 0.50%

Question 52

You have an interest rate of 8.44% compounded quarterly. What is the equivalent effective annual interest rate?

A) 7.81%
B) 7.71%
C) 8.71%
D) 8.91%
E) 9.71%

Question 53

Calculate the nominal rate of interest p.a. compounded semi-annually if $5000.00 accumulates to $7002.64 in 78 months.

A) 0.8656%
B) 0.02625%
C) 2.625%
D) 0.0525%
E) 5.25%