Question

Anne purchased a bond for a museum valued at $25,000 for $13,450. If the bond pays 7% annual interest compounded monthly, how long must she hold it until it reaches its full face value?

a) 10 years
b) 12 years
c) 15 years
d) 20 years

Answer 1

To calculate how long Anne must hold the bond until it reaches its full face value, we can use the compound interest formula. Plugging the given values into the formula, we find that Anne must hold the bond for approximately 10.4 years. Rounding to the closest whole number of years, the answer is 10 years (option a).

Step-by-step explanation:

To calculate how long Anne must hold the bond until it reaches its full face value, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the bond

P = the present value of the bond

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

Given that the present value of the bond is $13,450 and the future value is $25,000, the formula becomes:

25,000 = 13,450(1 + 0.07/12)^(12t)

Simplifying this equation, we get:

25,000/13,450 = (1 + 0.07/12)^(12t)

1.86 = (1.005833)^12t

Take the log base 1.005833 on both sides:

log(1.86) = log((1.005833)^12t)

Using logarithmic properties, we can bring the exponent down:

log(1.86) = 12t * log(1.005833)

Divide both sides by 12 * log(1.005833) to solve for t:

t = log(1.86) / (12 * log(1.005833))

Plugging the values into a calculator, we find that t ≈ 10.4 years.

Since the question asks for the closest whole number of years, the answer is 10 years (option a).