# MAT 108-Simple and Compound Interest Solutions

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```					      MAT 108 – Simple and Compound Interest Solutions

Compound Interest

Some relevant notation:

P    =   present value of investment
r    =   nominal interest rate
i   =   interest rate per compounding period
n    =   number of compounding periods
F    =   future value of investment

Some relevant equations:

F = P (1 + nr) (simple interest)
F = P (1 + i)n (compound interest)
ref f = (1 + i)n − 1 (compound interest)

1. For each of the following situations, compute i, the interest per com-
pounding period.

(a) 4% compounded monthly
(b) 4% compounded daily
(c) 8% compounded quarterly
(d) 8% compounded daily

2. If you invest \$500, determine how much your money will grow to under
each of the following scenarios

(a) The money grows at 6.2% compounded quarterly for 8 years.

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(b) The money grows at 10.2% compounded monthly for 8 years.
(c) The money grows at 2.8% compounded daily for 4 years.
(d) The money grows at 5.1% compounded daily for 14 years.

3. If you want to save \$5000, how much must you invest to achieve this
under each of the following scenarios.

(a) You have 7 years, and your money can earn 3.9% compounded
daily.
(b) You have 4 years, and your money can earn 5.3% compounded
daily.

4. If you invest \$1200, determine in each of the following scenarios how
long it will take for your investment to grow to a value of \$2000.

(a) The money grows at 6.2% compounded quarterly.
Answer: 33.12 quarters or 8.303 years.
(b) The money grows at 10.2% compounded monthly.
Answer: 60.35 months or 5.03 years.
(c) The money grows at 2.8% compounded daily.
Answer: 6,659.23 days or 18.24 years.
(d) The money grows at 5.1% compounded daily.
Answer: 3,585.86 days or 9.82 years.

5. What is the eﬀective rate of return in each of the following scenarios

(a) 4% compounded monthly
(b) 4% compounded daily

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(c) 8.4% compounded quarterly
(d) 8.4% compounded daily

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Increasing Annuities

Some relevant notation:

R    =   amount of periodic investment
r    =   nominal interest rate
i   =   interest rate per compounding period
n    =   number of compounding periods/investments
F    =   total future value of investment

Some relevant equations:

(1 + i)n − 1
sn i =
i
F = sn i R

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