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

$41,770.55

Explanation:

Compound Interest Formula

`\large \text{$ \sf A=P\left(1+(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+(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=(50000)/(\left(1.001875)\right)^(96)}`

`\implies \sf P=(50000)/(1.19701560...)`

`\implies \sf P=41770.55`

Therefore, Matilda should deposit $41,770.55.

Answer 2

• $41771.09

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`