Anthony invested 36,000 in an account paying an interest rate of 5.3% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach 51,800?

Solution

A n t h o n y in v es t e d 36, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 5.3% co m p o u n d e d q u a r t er l y . A ss u min g n o d e p os i t s or w i t h d r a w a l s a re ma d e, h o w l o n g w o u l d i t t ak e, t o t h e n e a res t ye a r, f or t h e v a l u e o f t h e a cco u n t t o re a c h 51, 800 ?

Time : 6.91

Solution steps

Translate the problem into an equation:

51800 = 36000 (1 + \frac{0.053}{4})^{4 t}

Solve for

t, 51800 = 36000 (1 + \frac{0.053}{4})^{4 t} : t = 6.91

Time : 6.91