Question

Matilda wants to have $50,000 available in 8 years for future repairs on her home.  How much should she deposit into an account that yields 2.25% interest compounded monthly in order to have that amount?

Answer 1

Answer:

• $41771.09

Step-by-step explanation:

Given

• Time t = 8 years,
• Interest rate r = 2.25% = 0.0225,
• Number of compounds n = 12 per year,
• Final amount F = $50000.

To find

• Amount of deposit P = ?

Solution

Use the compound equation:

• $F=P(1+r/n)^{nt}$

Plug in the values and solve for P:

• $50000=P(1+0.0225/12)^{8*12}$
• $50000=P(1+0.0225/12)^{96}$
• $50000=1.197P$
• $P=50000/1.197$
• $P=41771.09$

Answer 2

Answer:

$41,770.55

Step-by-step explanation:

Compound Interest Formula

$\large \text{ \sf A=P\left(1+\frac{r}{n}\right)^{nt} }$

where:

• A = Final amount.
• P = Principal amount.
• r = Interest rate (in decimal form).
• n = Number of times interest is applied per year.
• t = Time (in years).

Given values:

• A = $50,000
• r = 2.25% = 0.0225
• n = 12 (monthly)
• t = 8 years

Substitute the given values into the formula and solve for P:

$\implies \sf 50000=P\left(1+\frac{0.0225}{12}\right)^{12 \cdot 8}$

$\implies \sf 50000=P\left(1+0.001875}\right)^{96}$

$\implies \sf 50000=P\left(1.001875}\right)^{96}$

$\implies \sf P=\dfrac{50000}{\left(1.001875}\right)^{96}}$

$\implies \sf P=\dfrac{50000}{1.19701560...}$

$\implies \sf P=41770.55$

Therefore, Matilda should deposit $41,770.55.